About this quiz
A new set of 20 mental ability questions from the whole Loksewa Pathsala question bank every time you start.
This Lok Sewa practice set has 281 multiple-choice questions (Subject: Maths and IQ · For: Kharidar, Nayab Subba, Section Officer · Level: Medium). Take the quiz above first; after that, use the study list below to revise every question with its correct answer and a short explanation.
Study list: all 281 questions with answers and explanations
Written as a fraction in its lowest terms, 35% is equal to which of the following?
- A) 7/20 ✔
- B) 7/10
- C) 3/5
- D) 35/10
Why: 35% = 35/100; dividing top and bottom by 5 gives 7/20.
The fraction 3/8 is equal to what percent?
- A) 30%
- B) 37.5% ✔
- C) 35%
- D) 38.5%
Why: 3/8 × 100 = 300/8 = 37.5%.
The decimal 0.08 written as a percent is:
- A) 80%
- B) 0.8%
- C) 0.08%
- D) 8% ✔
Why: Move the decimal point two places to the right: 0.08 × 100 = 8%.
Which fraction is equal to 16 2/3%?
- A) 1/5
- B) 1/6 ✔
- C) 1/8
- D) 2/3
Why: 1/6 × 100 = 100/6 = 16 2/3%.
Find 18% of Rs 3,500.
- A) Rs 630 ✔
- B) Rs 580
- C) Rs 650
- D) Rs 540
Why: 18/100 × 3,500 = 18 × 35 = Rs 630.
45% of a sum of money is Rs 540. What is the whole sum?
- A) Rs 1,080
- B) Rs 1,150
- C) Rs 2,430
- D) Rs 1,200 ✔
Why: Whole = 540 × 100 / 45 = 54,000 / 45 = Rs 1,200.
What percent of Rs 2,500 is Rs 375?
- A) 12%
- B) 12.5%
- C) 15% ✔
- D) 18%
Why: 375 / 2,500 × 100 = 15%.
A student scores 63 marks out of 90. What is the percentage score?
- A) 72%
- B) 63%
- C) 70% ✔
- D) 68%
Why: 63 / 90 × 100 = 0.7 × 100 = 70%.
A's income is 20% more than B's income. By what percent is B's income less than A's?
- A) 16 2/3% ✔
- B) 18%
- C) 20%
- D) 25%
Why: B is less than A by 20/(100 + 20) × 100 = 20/120 × 100 = 16 2/3%.
The price of a jacket rises from Rs 1,200 to Rs 1,500. What is the percent increase?
- A) 20%
- B) 300%
- C) 30%
- D) 25% ✔
Why: Increase = 300; 300 / 1,200 × 100 = 25%. The base is the original price.
The price of a pressure cooker falls from Rs 640 to Rs 560. What is the percent decrease?
- A) 14.3%
- B) 12.5% ✔
- C) 10%
- D) 8%
Why: Decrease = 80; 80 / 640 × 100 = 12.5%.
A monthly salary of Rs 30,000 is increased by 12%. What is the new salary?
- A) Rs 30,360
- B) Rs 33,000
- C) Rs 34,200
- D) Rs 33,600 ✔
Why: 30,000 × 112/100 = Rs 33,600.
To decrease a value by 15% in one step, you multiply it by which factor?
- A) 0.15
- B) 0.85 ✔
- C) 1.15
- D) 0.75
Why: Decrease by 15% means × (100 − 15)/100 = × 0.85.
A price is first increased by 30% and then decreased by 20%. What is the net effect?
- A) 4% increase ✔
- B) 6% increase
- C) 10% increase
- D) 4% decrease
Why: Net = 30 − 20 + (30 × −20)/100 = 10 − 6 = 4%, a net increase.
A price is raised by 20% and then the new price is reduced by 20%. What is the net result?
- A) No change
- B) 2% decrease
- C) 4% decrease ✔
- D) 4% increase
Why: 20 − 20 + (20 × −20)/100 = −4, so a net decrease of 4% (r²/100 = 400/100 = 4).
Rs 8,000 is increased by 10% and then the new amount is again increased by 10%. What is the final amount?
- A) Rs 9,600
- B) Rs 9,680 ✔
- C) Rs 9,800
- D) Rs 9,580
Why: 8,000 × 1.1 = 8,800; 8,800 × 1.1 = Rs 9,680 (a 21% total rise).
The population of a municipality is 50,000 and it grows at 4% per year. What will it be after 2 years?
- A) 54,000
- B) 52,080
- C) 54,160
- D) 54,080 ✔
Why: 50,000 × 1.04 × 1.04 = 52,000 × 1.04 = 54,080.
A motorbike bought for Rs 80,000 loses 20% of its value every year. What is its value after 2 years?
- A) Rs 51,200 ✔
- B) Rs 56,000
- C) Rs 48,000
- D) Rs 64,000
Why: 80,000 × 0.8 = 64,000; 64,000 × 0.8 = Rs 51,200.
The price of rice rises by 20%. By what percent must a family cut its consumption so that its expense on rice stays the same?
- A) 20%
- B) 25%
- C) 16 2/3% ✔
- D) 15%
Why: Cut = 20/(100 + 20) × 100 = 20/120 × 100 = 16 2/3%.
The population of a town is now 26,450. It has grown at 15% per year for the last 2 years. What was it 2 years ago?
- A) 20,000 ✔
- B) 19,500
- C) 21,000
- D) 22,000
Why: 26,450 ÷ (1.15 × 1.15) = 26,450 ÷ 1.3225 = 20,000. Check: 20,000 to 23,000 to 26,450.
Using the fraction table, 12.5% of Rs 960 is:
- A) Rs 96
- B) Rs 160
- C) Rs 125
- D) Rs 120 ✔
Why: 12.5% = 1/8, and 960 ÷ 8 = Rs 120.
Using the swap trick, 4% of 75 is equal to:
- A) 4
- B) 30
- C) 3 ✔
- D) 0.3
Why: 4% of 75 = 75% of 4 = 3/4 × 4 = 3.
What is 5% of Rs 4,820?
- A) Rs 482
- B) Rs 241 ✔
- C) Rs 251
- D) Rs 24.10
Why: 10% of 4,820 = 482, and 5% is half of that, Rs 241.
On which price is a discount always calculated?
- A) Cost price
- B) Marked price ✔
- C) Selling price
- D) Price after VAT
Why: Discount is the reduction given on the marked (list) price, so the discount percent uses MP as the base.
A trader buys a TV for Rs 18,000, pays Rs 500 for transport and Rs 1,500 for repair, and sells it for Rs 22,000. What is his profit?
- A) Rs 4,000
- B) Rs 3,500
- C) Rs 2,000 ✔
- D) Rs 2,500
Why: CP = 18,000 + 500 + 1,500 = 20,000; profit = 22,000 − 20,000 = Rs 2,000.
An article bought for Rs 1,600 is sold for Rs 2,000. What is the profit percent?
- A) 25% ✔
- B) 20%
- C) 40%
- D) 24%
Why: Profit = 400; 400 / 1,600 × 100 = 25%. Profit percent is on CP, not SP.
A cupboard bought for Rs 2,500 is sold for Rs 2,150. What is the loss percent?
- A) 15%
- B) 35%
- C) 12%
- D) 14% ✔
Why: Loss = 350; 350 / 2,500 × 100 = 14%.
The cost price of 15 notebooks is equal to the selling price of 12 notebooks. What is the profit percent?
- A) 20%
- B) 25% ✔
- C) 30%
- D) 3%
Why: Profit = (15 − 12)/12 × 100 = 3/12 × 100 = 25%.
A shopkeeper buys a fan for Rs 1,250 and wants a profit of 12%. At what price should he sell it?
- A) Rs 1,400 ✔
- B) Rs 1,262
- C) Rs 1,350
- D) Rs 1,100
Why: SP = 1,250 × 112/100 = Rs 1,400.
A table bought for Rs 3,200 is sold at a loss of 15%. What is the selling price?
- A) Rs 2,880
- B) Rs 3,680
- C) Rs 2,720 ✔
- D) Rs 2,780
Why: SP = 3,200 × 85/100 = Rs 2,720.
A mobile set is sold for Rs 2,875 at a profit of 15%. What was its cost price?
- A) Rs 2,443.75
- B) Rs 2,600
- C) Rs 2,750
- D) Rs 2,500 ✔
Why: CP = 2,875 × 100/115 = Rs 2,500. (Taking 15% off the SP gives the wrong answer.)
A chair is sold for Rs 1,710 at a loss of 10%. What was its cost price?
- A) Rs 1,900 ✔
- B) Rs 1,881
- C) Rs 1,800
- D) Rs 1,539
Why: CP = 1,710 × 100/90 = Rs 1,900.
A jacket is marked Rs 3,600 and sold at a discount of 15%. What is the selling price?
- A) Rs 3,240
- B) Rs 3,060 ✔
- C) Rs 540
- D) Rs 3,100
Why: Discount = 15% of 3,600 = 540; SP = 3,600 − 540 = Rs 3,060.
A rice cooker marked Rs 2,400 is sold for Rs 2,040. What is the discount percent?
- A) 18%
- B) 12%
- C) 15% ✔
- D) 17.6%
Why: Discount = 360; 360 / 2,400 × 100 = 15%. Discount percent is on MP.
An article costs Rs 2,000. The seller wants a profit of 20% even after giving a 20% discount. What price should he mark?
- A) Rs 2,880
- B) Rs 2,800
- C) Rs 3,000 ✔
- D) Rs 3,200
Why: SP = 2,000 × 1.2 = 2,400; MP × 0.8 = 2,400, so MP = 2,400 × 100/80 = Rs 3,000.
Successive discounts of 25% and 10% are equal to a single discount of:
- A) 35%
- B) 32.5% ✔
- C) 32%
- D) 30%
Why: 25 + 10 − (25 × 10)/100 = 35 − 2.5 = 32.5%.
A carpet marked Rs 6,000 is sold after successive discounts of 10% and 5%. What is the selling price?
- A) Rs 5,100
- B) Rs 5,160
- C) Rs 5,400
- D) Rs 5,130 ✔
Why: 6,000 × 0.9 = 5,400; 5,400 × 0.95 = Rs 5,130.
Two successive discounts of 15% each are equal to a single discount of:
- A) 30%
- B) 27.5%
- C) 27.75% ✔
- D) 28.25%
Why: 15 + 15 − (15 × 15)/100 = 30 − 2.25 = 27.75%.
Two articles are each sold for Rs 1,200, one at 20% profit and the other at 20% loss. What is the overall result?
- A) 4% loss ✔
- B) No profit, no loss
- C) 4% profit
- D) 2% loss
Why: With the same SP and equal profit and loss percent, there is always a loss of r²/100 = 400/100 = 4%.
Two phones are sold for Rs 4,800 each, one at 20% profit and the other at 20% loss. What is the total loss in rupees?
- A) Nothing
- B) Rs 200
- C) Rs 960
- D) Rs 400 ✔
Why: CPs are 4,800 × 100/120 = 4,000 and 4,800 × 100/80 = 6,000. Total CP 10,000, total SP 9,600, loss Rs 400.
At 13 percent VAT, how much does a customer pay for an item priced Rs 5,000 before VAT?
- A) Rs 5,130
- B) Rs 5,650 ✔
- C) Rs 5,600
- D) Rs 6,300
Why: VAT = 5,000 × 13/100 = 650; amount = 5,000 + 650 = Rs 5,650.
A bill of Rs 6,780 includes 13 percent VAT. What was the price before VAT?
- A) Rs 5,898.60
- B) Rs 5,900
- C) Rs 6,000 ✔
- D) Rs 6,767
Why: Price = 6,780 × 100/113 = Rs 6,000. (Taking 13% off the bill gives the wrong answer.)
A bill of Rs 2,260 includes 13 percent VAT. How much of the bill is VAT?
- A) Rs 260 ✔
- B) Rs 293.80
- C) Rs 226
- D) Rs 300
Why: Price before VAT = 2,260 × 100/113 = 2,000, so VAT = 2,260 − 2,000 = Rs 260.
A heater is marked Rs 5,000. A discount of 20% is given and then 13 percent VAT is added. How much does the customer pay?
- A) Rs 4,650
- B) Rs 4,520 ✔
- C) Rs 5,650
- D) Rs 4,000
Why: After discount 5,000 × 0.8 = 4,000; with VAT 4,000 × 1.13 = Rs 4,520.
In a bill that has both a discount and VAT, VAT is normally calculated on which amount?
- A) The cost price
- B) The marked price
- C) The discount amount
- D) The price after discount ✔
Why: VAT is added after the discount, so it is worked out on the reduced price.
Find the next term: 6, 13, 20, 27, ?
- A) 34 ✔
- B) 33
- C) 35
- D) 41
Why: The difference is always +7, so 27 + 7 = 34.
Find the next term: 81, 72, 63, 54, ?
- A) 46
- B) 44
- C) 36
- D) 45 ✔
Why: Each term is 9 less than the one before: 54 − 9 = 45.
Find the next term: 3, 4, 7, 12, 19, ?
- A) 26
- B) 28 ✔
- C) 27
- D) 31
Why: Differences are 1, 3, 5, 7 (odd numbers), so the next difference is 9: 19 + 9 = 28.
Find the next term: 5, 15, 45, 135, ?
- A) 270
- B) 225
- C) 405 ✔
- D) 145
Why: Each term is multiplied by 3: 135 × 3 = 405.
Find the next term: 2, 2, 4, 12, 48, ?
- A) 240 ✔
- B) 96
- C) 192
- D) 144
Why: The multipliers are × 1, × 2, × 3, × 4, so the next is × 5: 48 × 5 = 240.
Find the next term: 8, 27, 64, 125, ?
- A) 196
- B) 225
- C) 256
- D) 216 ✔
Why: These are cubes of 2, 3, 4, 5, so the next is 6 × 6 × 6 = 216.
Find the next term: 3, 8, 15, 24, 35, ?
- A) 46
- B) 48 ✔
- C) 49
- D) 50
Why: Each term is one less than a square (4 − 1, 9 − 1, 16 − 1, 25 − 1, 36 − 1), so the next is 49 − 1 = 48. Differences 5, 7, 9, 11, 13 agree.
Find the next term: 19, 23, 29, 31, 37, ?
- A) 41 ✔
- B) 39
- C) 43
- D) 45
Why: These are consecutive prime numbers; the prime after 37 is 41 (39 = 3 × 13 is not prime, and 43 comes after 41).
Which of the following is NOT a prime number?
- A) 41
- B) 43
- C) 47
- D) 51 ✔
Why: 51 = 3 × 17, so it has more than two factors. 41, 43 and 47 are primes.
Find the next term: 3, 20, 6, 30, 9, 40, ?
- A) 50
- B) 10
- C) 12 ✔
- D) 45
Why: Odd places go 3, 6, 9 (add 3) and even places go 20, 30, 40. The next term is in an odd place: 9 + 3 = 12.
Find the next term: 4, 12, 10, 30, 28, ?
- A) 26
- B) 84 ✔
- C) 56
- D) 90
Why: The operations alternate × 3 and − 2: 4 × 3 = 12, 12 − 2 = 10, 10 × 3 = 30, 30 − 2 = 28, so next is 28 × 3 = 84.
Find the next term: 3, 7, 15, 31, 63, ?
- A) 126
- B) 125
- C) 95
- D) 127 ✔
Why: Rule: × 2 then + 1. 63 × 2 + 1 = 127.
Find the wrong term in the series: 2, 6, 18, 54, 160, 486
- A) 160 ✔
- B) 18
- C) 54
- D) 486
Why: Each term should be × 3: 54 × 3 = 162, not 160. Then 162 × 3 = 486 fits.
What is the position of the letter R in the English alphabet?
- A) 17
- B) 19
- C) 18 ✔
- D) 9
Why: Counting from A = 1 (or from O = 15 using EJOTY), R is the 18th letter. Its reverse position is 9.
Find the next term: C, F, I, L, ?
- A) N
- B) O ✔
- C) P
- D) M
Why: Positions are 3, 6, 9, 12 (add 3), so the next is 15, which is O.
Find the next term: Y, V, S, P, ?
- A) M ✔
- B) N
- C) L
- D) O
Why: Positions are 25, 22, 19, 16 (subtract 3), so the next is 13, which is M.
Which letter is the opposite partner of H (A pairs with Z, B with Y, and so on)?
- A) R
- B) T
- C) Q
- D) S ✔
Why: H is at position 8; its partner is at 27 − 8 = 19, which is S.
If LION is coded as MJPO, how is TIGER coded?
- A) SHFDQ
- B) UJHER
- C) UJHFS ✔
- D) UIHFS
Why: Each letter moves +1 (L to M, I to J, O to P, N to O). So T, I, G, E, R become U, J, H, F, S.
If WATER is coded as YCVGT, how is FIRE coded?
- A) GJSF
- B) HKTG ✔
- C) HKSG
- D) DGPC
Why: Each letter moves +2 (W to Y, A to C, T to V, E to G, R to T). So F, I, R, E become H, K, T, G.
In a code each letter is replaced by its opposite letter (A by Z, B by Y and so on). How is FACE written?
- A) UZXW
- B) VZXU
- C) GBDF
- D) UZXV ✔
Why: Use 27 minus the position: F 6 to U 21, A 1 to Z 26, C 3 to X 24, E 5 to V 22. So FACE becomes UZXV.
If MANGO is written as OGNAM, how is APPLE written?
- A) ELPPA ✔
- B) EPLPA
- C) APPLE
- D) ELPAP
Why: The letters are simply written in reverse order: A, P, P, L, E becomes E, L, P, P, A.
If BAG is coded as 10 because 2 + 1 + 7 = 10, what is the code for HEN?
- A) 25
- B) 26
- C) 27 ✔
- D) 28
Why: H = 8, E = 5, N = 14, and 8 + 5 + 14 = 27.
If "red" is called "blue", "blue" is called "green" and "green" is called "yellow", what is the colour of a clear sky called?
- A) Blue
- B) Green ✔
- C) Yellow
- D) Red
Why: A clear sky is really blue, and in this code "blue" is called "green", so the answer is green.
If SEND is coded as TGQH, how is CODE coded?
- A) DPEF
- B) DQFI
- C) EQGI
- D) DQGI ✔
Why: The shift grows with position: +1, +2, +3, +4 (S to T, E to G, N to Q, D to H). So C+1 = D, O+2 = Q, D+3 = G, E+4 = I, giving DQGI.
Hari borrows Rs 6,000 and pays back Rs 7,080 in total. How much interest did he pay?
- A) Rs 1,180
- B) Rs 1,080 ✔
- C) Rs 980
- D) Rs 7,080
Why: Interest = amount − principal = 7,080 − 6,000 = Rs 1,080.
What is the simple interest on Rs 7,500 at 8% per annum for 3 years?
- A) Rs 600
- B) Rs 1,600
- C) Rs 1,800 ✔
- D) Rs 2,400
Why: SI = 7,500 × 3 × 8/100 = Rs 1,800.
A sum earns Rs 2,700 as simple interest in 3 years at 12% per annum. What is the sum?
- A) Rs 9,720
- B) Rs 6,750
- C) Rs 8,100
- D) Rs 7,500 ✔
Why: P = 2,700 × 100/(3 × 12) = 270,000/36 = Rs 7,500.
Rs 12,000 earns Rs 3,600 simple interest in 5 years. What is the rate per annum?
- A) 5%
- B) 6% ✔
- C) 7.5%
- D) 30%
Why: R = 3,600 × 100/(12,000 × 5) = 6%.
In how many years will Rs 8,000 earn Rs 1,800 simple interest at 7.5% per annum?
- A) 3 years ✔
- B) 4 years
- C) 2.5 years
- D) 2.25 years
Why: T = 1,800 × 100/(8,000 × 7.5) = 180,000/60,000 = 3 years.
A sum amounts to Rs 11,200 in 4 years at 10% per annum simple interest. What is the sum?
- A) Rs 10,080
- B) Rs 7,200
- C) Rs 8,000 ✔
- D) Rs 8,400
Why: P = A × 100/(100 + R × T) = 11,200 × 100/140 = Rs 8,000.
At simple interest a sum amounts to Rs 6,600 in 2 years and Rs 7,200 in 4 years. What is the principal?
- A) Rs 6,300
- B) Rs 5,400
- C) Rs 4,800
- D) Rs 6,000 ✔
Why: Interest for 2 extra years = 600, so 300 per year. P = 6,600 − 2 × 300 = Rs 6,000.
At 12.5% per annum simple interest, in how many years will a sum double itself?
- A) 12.5 years
- B) 10 years
- C) 8 years ✔
- D) 16 years
Why: T = (2 − 1) × 100/12.5 = 8 years.
At 8% per annum simple interest, in how many years will a sum become three times itself?
- A) 12.5 years
- B) 25 years ✔
- C) 37.5 years
- D) 24 years
Why: Interest needed = 2 × P, so T = 2 × 100/8 = 25 years.
A sum doubles itself in 10 years at simple interest. In how many years will it become 4 times itself at the same rate?
- A) 30 years ✔
- B) 20 years
- C) 40 years
- D) 25 years
Why: Rate = 100/10 = 10%. For 4 times, interest = 3 × P, so T = 3 × 100/10 = 30 years.
What is the simple interest on Rs 15,000 at 8% per annum for 7 months?
- A) Rs 8,400
- B) Rs 840
- C) Rs 750
- D) Rs 700 ✔
Why: SI = 15,000 × 7/12 × 8/100 = 1,250 × 7 × 8/100 = Rs 700.
What is the simple interest on Rs 14,600 at 10% per annum for 146 days?
- A) Rs 1,460
- B) Rs 584 ✔
- C) Rs 365
- D) Rs 5,840
Why: T = 146/365 = 0.4 year; SI = 14,600 × 0.4 × 10/100 = Rs 584.
Find the simple interest on Rs 6,400 at 12% per annum for 2 years 3 months.
- A) Rs 1,536
- B) Rs 1,600
- C) Rs 1,792
- D) Rs 1,728 ✔
Why: T = 2 + 3/12 = 2.25 years; SI = 6,400 × 2.25 × 12/100 = Rs 1,728.
What amount will Rs 5,000 become in 2 years at 10% per annum compounded yearly?
- A) Rs 6,050 ✔
- B) Rs 6,000
- C) Rs 5,500
- D) Rs 6,100
Why: A = 5,000 × 1.1 × 1.1 = 5,000 × 1.21 = Rs 6,050.
Find the compound interest on Rs 12,000 at 5% per annum for 2 years, compounded yearly.
- A) Rs 1,200
- B) Rs 13,230
- C) Rs 1,230 ✔
- D) Rs 1,260
Why: A = 12,000 × 1.05 × 1.05 = 13,230; CI = 13,230 − 12,000 = Rs 1,230.
Find the compound interest on Rs 10,000 at 10% per annum for 3 years, compounded yearly.
- A) Rs 3,000
- B) Rs 3,310 ✔
- C) Rs 3,210
- D) Rs 13,310
Why: A = 10,000 × 1.1³ = 10,000 × 1.331 = 13,310; CI = Rs 3,310.
What will Rs 16,000 amount to in 3 years at 5% per annum compounded yearly?
- A) Rs 18,522 ✔
- B) Rs 18,400
- C) Rs 18,700
- D) Rs 2,522
Why: A = 16,000 × 1.05³ = 16,000 × 1.157625 = Rs 18,522.
On Rs 10,000 at 10% per annum compounded yearly, what is the interest for the second year only?
- A) Rs 1,000
- B) Rs 2,100
- C) Rs 1,210
- D) Rs 1,100 ✔
Why: After year 1 the sum is 11,000; interest for year 2 = 11,000 × 10/100 = Rs 1,100.
Find the compound interest on Rs 20,000 for 1 year at 8% per annum, compounded half-yearly.
- A) Rs 1,600
- B) Rs 1,664
- C) Rs 1,632 ✔
- D) Rs 21,632
Why: Rate per half-year = 4%, periods = 2. A = 20,000 × 1.04 × 1.04 = 21,632; CI = Rs 1,632.
Interest at 12% per annum is compounded half-yearly for 2 years. What are the rate per period and the number of periods?
- A) 6% and 4 periods ✔
- B) 12% and 2 periods
- C) 6% and 2 periods
- D) 24% and 4 periods
Why: Half-yearly: rate = 12/2 = 6% per half-year and periods = 2 × 2 = 4.
What is the difference between compound interest and simple interest on Rs 15,000 for 2 years at 8% per annum?
- A) Rs 120
- B) Rs 96 ✔
- C) Rs 960
- D) Rs 64
Why: Difference = P × (R/100)² = 15,000 × 0.08 × 0.08 = 15,000 × 0.0064 = Rs 96.
The difference between CI and SI on a sum for 2 years at 6% per annum is Rs 72. What is the sum?
- A) Rs 12,000
- B) Rs 1,200
- C) Rs 24,000
- D) Rs 20,000 ✔
Why: P = 72 ÷ (6/100)² = 72 ÷ 0.0036 = Rs 20,000.
Rs 6,250 amounts to Rs 7,290 in 2 years at compound interest, compounded yearly. What is the rate per annum?
- A) 10%
- B) 9%
- C) 8% ✔
- D) 8.5%
Why: (1 + R/100)² = 7,290/6,250 = 1.1664 = 1.08 × 1.08, so R = 8%.
What is the difference between CI (compounded yearly) and SI on Rs 8,000 at 10% per annum for 1 year?
- A) Rs 0 ✔
- B) Rs 80
- C) Rs 8
- D) Rs 800
Why: For the first year CI and SI are equal: both are 8,000 × 10/100 = 800, so the difference is Rs 0.
What is the ratio of Rs 2.50 to 75 paisa in its simplest form?
- A) 3 : 10
- B) 10 : 3 ✔
- C) 1 : 3
- D) 5 : 3
Why: Change both to paisa: 250 : 75. Divide by 25: 10 : 3.
What is the simplest form of 84 : 126?
- A) 3 : 2
- B) 3 : 4
- C) 2 : 3 ✔
- D) 4 : 5
Why: HCF of 84 and 126 is 42. 84 ÷ 42 = 2 and 126 ÷ 42 = 3, so 2 : 3.
Write 2/3 : 3/4 in its simplest form.
- A) 8 : 9 ✔
- B) 9 : 8
- C) 2 : 3
- D) 3 : 4
Why: Multiply both terms by the LCM 12: 2/3 × 12 = 8 and 3/4 × 12 = 9, so 8 : 9.
What is the simplest form of 0.6 : 1.5?
- A) 3 : 5
- B) 5 : 2
- C) 6 : 5
- D) 2 : 5 ✔
Why: Multiply by 10: 6 : 15. Divide by 3: 2 : 5.
Which order arranges 3 : 4, 5 : 7 and 7 : 10 from smallest to largest?
- A) 3 : 4, 5 : 7, 7 : 10
- B) 5 : 7, 7 : 10, 3 : 4
- C) 7 : 10, 3 : 4, 5 : 7
- D) 7 : 10, 5 : 7, 3 : 4 ✔
Why: As decimals: 3 : 4 = 0.75, 5 : 7 = about 0.714, 7 : 10 = 0.7. Smallest to largest: 7 : 10, 5 : 7, 3 : 4.
What number must be added to each term of 5 : 9 to make it 3 : 5?
- A) 1 ✔
- B) 2
- C) 3
- D) 4
Why: (5 + x)/(9 + x) = 3/5, so 25 + 5x = 27 + 3x and x = 1. Check: 6 : 10 = 3 : 5.
Rs 24,000 is divided between two brothers in the ratio 5 : 7. What is the smaller share?
- A) Rs 14,000
- B) Rs 10,000 ✔
- C) Rs 12,000
- D) Rs 9,600
Why: Total parts = 12, one part = 24,000 ÷ 12 = 2,000. Smaller share = 5 × 2,000 = Rs 10,000.
Rs 27,000 is divided among A, B and C in the ratio 2 : 3 : 4. What is C's share?
- A) Rs 9,000
- B) Rs 6,000
- C) Rs 12,000 ✔
- D) Rs 13,500
Why: Total parts = 9, one part = 27,000 ÷ 9 = 3,000. C's share = 4 × 3,000 = Rs 12,000.
Two shares are in the ratio 5 : 8 and the larger share is Rs 1,500 more than the smaller. What is the larger share?
- A) Rs 2,500
- B) Rs 6,500
- C) Rs 2,400
- D) Rs 4,000 ✔
Why: Difference = 8 − 5 = 3 parts = Rs 1,500, so one part = 500. Larger share = 8 × 500 = Rs 4,000.
If A : B = 3 : 4 and B : C = 6 : 7, what is A : B : C?
- A) 9 : 12 : 14 ✔
- B) 3 : 4 : 7
- C) 3 : 6 : 7
- D) 18 : 24 : 21
Why: Make B equal to 12: A : B = 9 : 12 and B : C = 12 : 14. So A : B : C = 9 : 12 : 14.
What is the compound ratio of 3 : 4, 8 : 9 and 3 : 2?
- A) 2 : 3
- B) 1 : 1 ✔
- C) 3 : 2
- D) 14 : 15
Why: (3 × 8 × 3) : (4 × 9 × 2) = 72 : 72 = 1 : 1.
What is the duplicate ratio of 5 : 7?
- A) 10 : 14
- B) 125 : 343
- C) 7 : 5
- D) 25 : 49 ✔
Why: Duplicate ratio = 5² : 7² = 25 : 49.
What is the sub-duplicate ratio of 81 : 144?
- A) 9 : 16
- B) 4 : 3
- C) 3 : 4 ✔
- D) 27 : 48
Why: Sub-duplicate ratio = √81 : √144 = 9 : 12 = 3 : 4.
In the proportion 6 : 15 = 10 : 25, which numbers are the means?
- A) 15 and 10 ✔
- B) 6 and 25
- C) 6 and 10
- D) 15 and 25
Why: The means are the inner terms, 15 and 10. Check: 15 × 10 = 150 = 6 × 25.
Find x if 9 : x = 12 : 20.
- A) 12
- B) 15 ✔
- C) 18
- D) 26.7
Why: Product of extremes = product of means: 9 × 20 = 12 × x, so 180 = 12x and x = 15.
What is the fourth proportional to 6, 9 and 14?
- A) 18
- B) 9.3
- C) 21 ✔
- D) 28
Why: Fourth proportional = b × c / a = 9 × 14/6 = 126/6 = 21.
What is the third proportional to 8 and 12?
- A) 16
- B) 24
- C) 20
- D) 18 ✔
Why: Third proportional = b²/a = 12 × 12/8 = 144/8 = 18.
What is the mean proportional between 9 and 49?
- A) 21 ✔
- B) 29
- C) 441
- D) 16
Why: Mean proportional = √(9 × 49) = √441 = 21.
15 kg of rice costs Rs 1,350. What will 22 kg of the same rice cost?
- A) Rs 2,025
- B) Rs 1,980 ✔
- C) Rs 1,850
- D) Rs 2,200
Why: Direct proportion. Price per kg = 1,350 ÷ 15 = Rs 90. Cost of 22 kg = 22 × 90 = Rs 1,980.
12 workers can finish a job in 15 days. In how many days can 18 workers finish it?
- A) 22.5 days
- B) 12 days
- C) 9 days
- D) 10 days ✔
Why: Inverse proportion. Total = 12 × 15 = 180 worker-days; 180 ÷ 18 = 10 days.
A bus at 45 km per hour takes 6 hours for a journey. How long will it take at 54 km per hour?
- A) 5 hours ✔
- B) 7.2 hours
- C) 4.5 hours
- D) 5.5 hours
Why: Distance = 45 × 6 = 270 km. Time at 54 km per hour = 270 ÷ 54 = 5 hours.
The ages of two friends are in the ratio 4 : 5 and their sum is 63 years. How old is the older friend?
- A) 28 years
- B) 30 years
- C) 35 years ✔
- D) 36 years
Why: Total parts = 9, one part = 63 ÷ 9 = 7. Older friend = 5 × 7 = 35 years.
The present ages of two brothers are in the ratio 3 : 5. After 6 years the ratio will be 9 : 13. What is the present age of the younger brother?
- A) 18 years
- B) 20 years
- C) 15 years
- D) 12 years ✔
Why: (3x + 6)/(5x + 6) = 9/13, so 39x + 78 = 45x + 54 and x = 4. Younger = 3 × 4 = 12 years. Check: 18 : 26 = 9 : 13.
60 litres of a mixture has milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 7 : 5?
- A) 6 litres
- B) 12 litres ✔
- C) 10 litres
- D) 18 litres
Why: Milk = 42 L, water = 18 L. Milk stays 42: 42/(18 + w) = 7/5, so 210 = 126 + 7w and w = 12 litres.
Sugar at Rs 90 per kg is mixed with sugar at Rs 110 per kg to make a mixture worth Rs 95 per kg. In what ratio are they mixed (cheaper to dearer)?
- A) 1 : 3
- B) 2 : 1
- C) 1 : 1
- D) 3 : 1 ✔
Why: Ratio = (110 − 95) : (95 − 90) = 15 : 5 = 3 : 1.
Sunita can finish a job in 15 days. What part of the job does she finish in 6 days?
- A) 1/6
- B) 2/5 ✔
- C) 3/5
- D) 2/3
Why: One day's work = 1/15. In 6 days: 6/15 = 2/5.
Ramesh does 1/8 of a job each day. How many days does he need to finish the whole job?
- A) 4 days
- B) 7 days
- C) 8 days ✔
- D) 16 days
Why: If one day's work is 1/n, the job takes n days. So 8 days.
A can do a piece of work in 10 days and B in 15 days. In how many days can they finish it together?
- A) 12.5 days
- B) 5 days
- C) 6 days ✔
- D) 25 days
Why: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so 6 days. Formula: 10 × 15/25 = 6.
A, B and C can do a job in 20, 30 and 60 days. In how many days can all three finish it together?
- A) 10 days ✔
- B) 15 days
- C) 12 days
- D) 36.7 days
Why: 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10, so 10 days.
A and B together can do a work in 10 days. A alone can do it in 15 days. How long will B alone take?
- A) 25 days
- B) 5 days
- C) 20 days
- D) 30 days ✔
Why: B's one day's work = 1/10 − 1/15 = 3/30 − 2/30 = 1/30, so 30 days.
A and B can do a job in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B and C take working together?
- A) 10 days ✔
- B) 5 days
- C) 15 days
- D) 8 days
Why: 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. This is 2 × (A + B + C), so A + B + C = 1/10, that is 10 days.
A can do half of a job in 5 days, and B can do the whole job in 15 days. In how many days can they finish the whole job together?
- A) 3.75 days
- B) 6 days ✔
- C) 10 days
- D) 7.5 days
Why: A needs 10 days for the full job. Together: 10 × 15/(10 + 15) = 150/25 = 6 days.
A takes 12 days and B takes 24 days to do a job. Using the LCM method with total work 24 units, how many units do they do together in one day?
- A) 2 units
- B) 4 units
- C) 36 units
- D) 3 units ✔
Why: A does 24 ÷ 12 = 2 units and B does 24 ÷ 24 = 1 unit a day. Together 3 units a day.
A can do a job in 12 days and B in 18 days. They work together for 4 days and then A leaves. In how many more days will B finish the job?
- A) 8 days ✔
- B) 10 days
- C) 12 days
- D) 6 days
Why: LCM = 36 units; A does 3, B does 2 a day. In 4 days: 4 × 5 = 20 units. Left: 16 units, B takes 16 ÷ 2 = 8 days.
A is twice as efficient as B. Together they finish a job in 12 days. How long would B alone take?
- A) 18 days
- B) 24 days
- C) 36 days ✔
- D) 48 days
Why: Efficiency A : B = 2 : 1. Total work = (2 + 1) × 12 = 36 units. B does 1 unit a day, so 36 days.
A can finish a job in 20 days. He works on it for 5 days, and B finishes the rest in 9 days. How long would B take to do the whole job alone?
- A) 15 days
- B) 12 days ✔
- C) 11.25 days
- D) 18 days
Why: A does 5/20 = 1/4. B does the remaining 3/4 in 9 days, so the whole job takes 9 × 4/3 = 12 days.
A can do a job in 9 days. B is 50% more efficient than A. How many days will B take alone?
- A) 13.5 days
- B) 4.5 days
- C) 3 days
- D) 6 days ✔
Why: Efficiency A : B = 2 : 3, so B's time = 2/3 of A's time = 9 × 2/3 = 6 days.
A can do a job in 12 days and B in 18 days. They work together and are paid Rs 6,000. What is A's share?
- A) Rs 3,600 ✔
- B) Rs 2,400
- C) Rs 3,000
- D) Rs 4,000
Why: LCM = 36; A does 3 and B does 2 units a day, ratio 3 : 2. A's share = 6,000 × 3/5 = Rs 3,600.
A takes 8 days and B takes 12 days to do a job. With the help of C they finish it in 4 days and are paid Rs 3,600. What is C's share?
- A) Rs 1,200
- B) Rs 900
- C) Rs 600 ✔
- D) Rs 400
Why: LCM = 24; A 3, B 2 units a day. All three do 24 ÷ 4 = 6 units a day, so C does 1. Ratio 3 : 2 : 1, so C gets 3,600 × 1/6 = Rs 600.
18 men can build a wall in 25 days. How many days will 30 men take to build the same wall?
- A) 41.7 days
- B) 15 days ✔
- C) 12 days
- D) 20 days
Why: M1 × D1 = M2 × D2: 18 × 25 = 30 × D2, so D2 = 450 ÷ 30 = 15 days.
20 men can complete a job in 12 days. How many more men must join so that the job is completed in 8 days?
- A) 30
- B) 8
- C) 12
- D) 10 ✔
Why: Men needed = 20 × 12/8 = 30. Extra men = 30 − 20 = 10.
15 men working 8 hours a day finish a job in 12 days. How many days will 20 men working 9 hours a day take for the same job?
- A) 10 days
- B) 9 days
- C) 8 days ✔
- D) 6 days
Why: Total = 15 × 8 × 12 = 1,440 man-hours. Days = 1,440 ÷ (20 × 9) = 1,440 ÷ 180 = 8 days.
10 men build a 40 m wall in 6 days. How many days will 15 men take to build a 90 m wall of the same kind?
- A) 9 days ✔
- B) 13.5 days
- C) 6 days
- D) 8 days
Why: D2 = M1 × D1 × W2/(W1 × M2) = 10 × 6 × 90/(40 × 15) = 5,400/600 = 9 days.
Pipe A fills a tank in 10 hours and pipe B fills it in 15 hours. If both are opened together, how long will they take to fill it?
- A) 12.5 hours
- B) 5 hours
- C) 25 hours
- D) 6 hours ✔
Why: 1/10 + 1/15 = 3/30 + 2/30 = 1/6, so 6 hours.
An inlet pipe fills a tank in 8 hours and an outlet pipe empties it in 12 hours. If both are opened together on an empty tank, when will it be full?
- A) 4.8 hours
- B) 24 hours ✔
- C) 20 hours
- D) 4 hours
Why: 1/8 − 1/12 = 3/24 − 2/24 = 1/24, so 24 hours.
Pipes A and B fill a tank in 12 and 15 hours, and pipe C empties it in 10 hours. If all three are opened on an empty tank, how long will it take to fill?
- A) 4 hours
- B) 12 hours
- C) 20 hours ✔
- D) 15 hours
Why: LCM = 60 units. Per hour: 5 + 4 − 6 = 3 units. Time = 60 ÷ 3 = 20 hours.
A pipe can fill a tank in 6 hours, but because of a leak it takes 8 hours. How long will the leak alone take to empty the full tank?
- A) 24 hours ✔
- B) 14 hours
- C) 2 hours
- D) 48 hours
Why: Leak's rate = 1/6 − 1/8 = 4/24 − 3/24 = 1/24, so 24 hours.
Pipe A fills a tank in 20 minutes and pipe B in 30 minutes. Both are opened for 6 minutes, then A is closed. How many more minutes will B take to fill the tank?
- A) 12 minutes
- B) 15 minutes ✔
- C) 18 minutes
- D) 24 minutes
Why: LCM = 60 units; A 3, B 2 units a minute. In 6 minutes: 6 × 5 = 30 units. Left 30 units, B takes 30 ÷ 2 = 15 minutes.
What is the average of 4, 8, 12, 16 and 20?
- A) 10
- B) 12 ✔
- C) 14
- D) 16
Why: Sum = 60, number = 5, so the average is 60 ÷ 5 = 12.
The average of the first 20 natural numbers is:
- A) 10
- B) 10.5 ✔
- C) 11
- D) 20
Why: Average of first n natural numbers = (n + 1) ÷ 2 = 21 ÷ 2 = 10.5.
The average of the first 10 even numbers is:
- A) 10
- B) 10.5
- C) 11 ✔
- D) 12
Why: Average of first n even numbers = n + 1 = 11. (2 + 4 + ... + 20 = 110; 110 ÷ 10 = 11)
The average of the first 15 odd numbers is:
- A) 15 ✔
- B) 16
- C) 14
- D) 30
Why: Average of first n odd numbers = n = 15.
The average of 8 numbers is 15. Their sum is:
- A) 23
- B) 100
- C) 120 ✔
- D) 150
Why: Sum = Average × Number = 15 × 8 = 120.
The average of 10 numbers is 30. If 5 is added to each number, the new average is:
- A) 30
- B) 35 ✔
- C) 50
- D) 80
Why: Adding 5 to every number adds 5 to the average: 30 + 5 = 35.
The average of 6 numbers is 12. If each number is multiplied by 4, the new average is:
- A) 16
- B) 24
- C) 48 ✔
- D) 72
Why: Multiplying every number by 4 multiplies the average by 4: 12 × 4 = 48.
The average age of 25 students is 12 years. When the teacher's age is included, the average becomes 13 years. The teacher's age is:
- A) 25 years
- B) 38 years ✔
- C) 13 years
- D) 40 years
Why: 26 × 13 = 338 and 25 × 12 = 300, so the teacher is 338 − 300 = 38 years.
The average weight of 10 men increases by 1.5 kg when one man weighing 60 kg is replaced by a new man. The new man weighs:
- A) 61.5 kg
- B) 70 kg
- C) 75 kg ✔
- D) 90 kg
Why: New = 60 + 10 × 1.5 = 60 + 15 = 75 kg.
The average of 5 numbers is 30. When one number is removed, the average of the rest is 28. The removed number is:
- A) 2
- B) 30
- C) 32
- D) 38 ✔
Why: 5 × 30 = 150 and 4 × 28 = 112, so the removed number is 150 − 112 = 38.
30 boys have an average of 50 marks and 20 girls have an average of 60 marks. The average of the whole class is:
- A) 54 ✔
- B) 55
- C) 56
- D) 52
Why: (30 × 50 + 20 × 60) ÷ 50 = (1,500 + 1,200) ÷ 50 = 2,700 ÷ 50 = 54.
A batsman scores 85 runs in his 15th innings and increases his average by 3. His average after the 15th innings is:
- A) 40
- B) 42
- C) 43 ✔
- D) 45
Why: 85 − 14 × 3 = 85 − 42 = 43. (Check: 14 × 40 + 85 = 645 = 15 × 43)
The average of 5 consecutive odd numbers is 25. The largest of them is:
- A) 27
- B) 29 ✔
- C) 31
- D) 33
Why: 25 is the middle number, so the numbers are 21, 23, 25, 27 and 29.
The average of three numbers is 24. Two of them are 16 and 35. The third number is:
- A) 21 ✔
- B) 24
- C) 25
- D) 19
Why: Sum = 3 × 24 = 72, so the third number = 72 − 16 − 35 = 21.
A is 5 years older than B, and the sum of their ages is 35 years. A's age is:
- A) 15 years
- B) 18 years
- C) 20 years ✔
- D) 25 years
Why: B = x, A = x + 5, so 2x + 5 = 35, x = 15 and A = 20.
The present ages of two brothers are in the ratio 3 : 4. After 6 years the ratio will be 4 : 5. The elder brother's present age is:
- A) 18 years
- B) 24 years ✔
- C) 20 years
- D) 30 years
Why: (3x + 6) ÷ (4x + 6) = 4 ÷ 5 gives 15x + 30 = 16x + 24, so x = 6; ages are 18 and 24.
A father is 4 times as old as his son. After 5 years he will be 3 times as old as his son. The father's present age is:
- A) 30 years
- B) 35 years
- C) 45 years
- D) 40 years ✔
Why: 4x + 5 = 3(x + 5) gives x = 10, so the father is 40.
The difference between the ages of two persons is 8 years now. After 10 years the difference will be:
- A) 18 years
- B) 8 years ✔
- C) 10 years
- D) 2 years
Why: The difference between two ages never changes.
A man's age 10 years hence will be twice his age 10 years ago. His present age is:
- A) 20 years
- B) 25 years
- C) 30 years ✔
- D) 40 years
Why: x + 10 = 2(x − 10) gives x + 10 = 2x − 20, so x = 30.
The average age of a husband and wife was 25 years when they married 4 years ago. Now, with one child, the average age of the family is 20 years. The child's age is:
- A) 2 years ✔
- B) 3 years
- C) 4 years
- D) 1 year
Why: Couple now = 2 × 25 + 2 × 4 = 58. Family total = 3 × 20 = 60, so the child is 60 − 58 = 2 years.
A speed of 90 km/h is equal to:
- A) 15 m/s
- B) 20 m/s
- C) 25 m/s ✔
- D) 30 m/s
Why: 90 × 5/18 = 25 m/s.
A speed of 20 m/s is equal to:
- A) 72 km/h ✔
- B) 60 km/h
- C) 54 km/h
- D) 36 km/h
Why: 20 × 18/5 = 72 km/h.
A car covers 300 km in 5 hours. Its speed is:
- A) 50 km/h
- B) 55 km/h
- C) 60 km/h ✔
- D) 65 km/h
Why: Speed = 300 ÷ 5 = 60 km/h.
A bus runs at 45 km/h for 3 hours 20 minutes. The distance covered is:
- A) 135 km
- B) 150 km ✔
- C) 145 km
- D) 160 km
Why: 3 hours 20 minutes = 10/3 hours; 45 × 10/3 = 150 km.
A man goes to a place at 30 km/h and returns at 20 km/h. His average speed for the whole journey is:
- A) 25 km/h
- B) 24 km/h ✔
- C) 22 km/h
- D) 26 km/h
Why: 2 × 30 × 20 ÷ (30 + 20) = 1,200 ÷ 50 = 24 km/h.
A car travels 100 km at 50 km/h and then 150 km at 75 km/h. Its average speed is:
- A) 62.5 km/h ✔
- B) 60 km/h
- C) 65 km/h
- D) 58 km/h
Why: Total time = 2 + 2 = 4 hours; average speed = 250 ÷ 4 = 62.5 km/h.
A train 180 m long runs at 54 km/h. The time it takes to pass a pole is:
- A) 10 seconds
- B) 15 seconds
- C) 18 seconds
- D) 12 seconds ✔
Why: 54 km/h = 15 m/s; 180 ÷ 15 = 12 seconds.
A train 240 m long at 72 km/h crosses a platform 160 m long. The time taken is:
- A) 12 seconds
- B) 20 seconds ✔
- C) 16 seconds
- D) 24 seconds
Why: 72 km/h = 20 m/s; distance = 240 + 160 = 400 m; 400 ÷ 20 = 20 seconds.
A train passes a pole in 15 seconds and a platform 100 m long in 25 seconds. The length of the train is:
- A) 100 m
- B) 120 m
- C) 150 m ✔
- D) 200 m
Why: L ÷ 15 = (L + 100) ÷ 25 gives 25L = 15L + 1,500, so L = 150 m.
Two trains 100 m and 150 m long run in opposite directions at 40 km/h and 50 km/h. The time they take to cross each other is:
- A) 10 seconds ✔
- B) 12 seconds
- C) 15 seconds
- D) 25 seconds
Why: Relative speed = 90 km/h = 25 m/s; distance = 250 m; 250 ÷ 25 = 10 seconds.
Two trains, each 100 m long, run in the same direction at 68 km/h and 50 km/h. The faster train passes the slower one in:
- A) 20 seconds
- B) 30 seconds
- C) 36 seconds
- D) 40 seconds ✔
Why: Relative speed = 18 km/h = 5 m/s; distance = 200 m; 200 ÷ 5 = 40 seconds.
A train 125 m long passes a man running at 5 km/h in the same direction in 10 seconds. The speed of the train is:
- A) 45 km/h
- B) 50 km/h ✔
- C) 55 km/h
- D) 60 km/h
Why: Relative speed = 12.5 m/s = 45 km/h; train speed = 45 + 5 = 50 km/h.
A boat goes 18 km/h downstream and 12 km/h upstream. Its speed in still water is:
- A) 3 km/h
- B) 6 km/h
- C) 15 km/h ✔
- D) 30 km/h
Why: Speed in still water = (18 + 12) ÷ 2 = 15 km/h.
A boat goes 20 km/h downstream and 14 km/h upstream. The speed of the stream is:
- A) 3 km/h ✔
- B) 6 km/h
- C) 17 km/h
- D) 7 km/h
Why: Speed of stream = (20 − 14) ÷ 2 = 3 km/h.
A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. Time to go 24 km downstream is:
- A) 3 hours
- B) 2.4 hours
- C) 2 hours ✔
- D) 2.5 hours
Why: Downstream speed = 12 km/h; 24 ÷ 12 = 2 hours.
A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. Time to go 24 km upstream is:
- A) 2 hours
- B) 2.4 hours
- C) 4 hours
- D) 3 hours ✔
Why: Upstream speed = 8 km/h; 24 ÷ 8 = 3 hours.
Two cities are 200 km apart. Two cars start at the same time towards each other at 45 km/h and 55 km/h. They meet after:
- A) 2 hours ✔
- B) 2.5 hours
- C) 4 hours
- D) 1.5 hours
Why: Relative speed = 100 km/h; 200 ÷ 100 = 2 hours.
The speeds of A and B are in the ratio 2 : 3. The ratio of the times they take to cover the same distance is:
- A) 2 : 3
- B) 3 : 2 ✔
- C) 4 : 9
- D) 9 : 4
Why: For a fixed distance, time is inversely proportional to speed, so 3 : 2.
Walking at 5 km/h a man is 7 minutes late; at 6 km/h he is 5 minutes early. The distance is:
- A) 5 km
- B) 8 km
- C) 6 km ✔
- D) 10 km
Why: Time difference = 12 minutes = 1/5 hour. D/5 − D/6 = 1/5 gives D/30 = 1/5, so D = 6 km.
A car covers a distance in 6 hours at 40 km/h. To cover the same distance in 4 hours, its speed must be:
- A) 50 km/h
- B) 55 km/h
- C) 60 km/h ✔
- D) 80 km/h
Why: Distance = 40 × 6 = 240 km; 240 ÷ 4 = 60 km/h.
Doctor : Hospital :: Teacher : ?
- A) School ✔
- B) Book
- C) Student
- D) Chalk
Why: A doctor works in a hospital; a teacher works in a school (worker and workplace).
Cow : Calf :: Dog : ?
- A) Kitten
- B) Puppy ✔
- C) Cub
- D) Foal
Why: A calf is the young one of a cow; a puppy is the young one of a dog.
Bee : Hive :: Spider : ?
- A) Den
- B) Nest
- C) Web ✔
- D) Burrow
Why: A bee lives in a hive; a spider lives in a web (animal and home).
Thermometer : Temperature :: Barometer : ?
- A) Humidity
- B) Atmospheric pressure ✔
- C) Earthquake
- D) Speed
Why: A barometer measures atmospheric pressure, just as a thermometer measures temperature.
Length : Metre :: Electric current : ?
- A) Volt
- B) Watt
- C) Ohm
- D) Ampere ✔
Why: The SI unit of length is the metre; the SI unit of electric current is the ampere.
Nepal : Kathmandu :: Japan : ?
- A) Osaka
- B) Kyoto
- C) Tokyo ✔
- D) Seoul
Why: Country and capital. Tokyo is the capital of Japan.
4 : 16 :: 7 : ?
- A) 14
- B) 49 ✔
- C) 28
- D) 56
Why: The second number is the square of the first: 7 × 7 = 49.
3 : 27 :: 5 : ?
- A) 15
- B) 25
- C) 75
- D) 125 ✔
Why: The second number is the cube of the first: 5 × 5 × 5 = 125.
5 : 24 :: 9 : ?
- A) 80 ✔
- B) 81
- C) 72
- D) 90
Why: 5² − 1 = 24, so the rule is square minus 1: 9² − 1 = 80.
ACE : BDF :: KMO : ?
- A) LMN
- B) LNP ✔
- C) JLN
- D) KNP
Why: Each letter moves forward by one: K to L, M to N, O to P.
AZ : BY :: CX : ?
- A) DV
- B) EW
- C) DW ✔
- D) DX
Why: These are opposite letter pairs. The opposite of D is W (4 + 23 = 27).
Find the odd one out: Apple, Mango, Potato, Banana
- A) Apple
- B) Mango
- C) Potato ✔
- D) Banana
Why: Potato is a vegetable; the others are fruits.
Find the odd one out: Mercury, Venus, Moon, Mars
- A) Mercury
- B) Venus
- C) Mars
- D) Moon ✔
Why: The Moon is a natural satellite of the Earth; the others are planets.
Find the odd one out: 2, 3, 5, 9, 11
- A) 9 ✔
- B) 3
- C) 5
- D) 11
Why: 9 = 3 × 3 is not a prime number; the others are primes.
Find the odd one out: 16, 25, 36, 48, 64
- A) 25
- B) 48 ✔
- C) 36
- D) 64
Why: 48 is not a perfect square; the others are 4², 5², 6² and 8².
Find the odd one out: BCD, FGH, JKL, MNP
- A) BCD
- B) FGH
- C) JKL
- D) MNP ✔
Why: The others are three consecutive letters; in MNP the letter O is skipped.
Find the odd one out: Rupee, Dollar, Euro, Tokyo
- A) Rupee
- B) Tokyo ✔
- C) Dollar
- D) Euro
Why: Tokyo is a city; the others are currencies.
Petal : Flower :: Page : ?
- A) Pen
- B) Library
- C) Book ✔
- D) Writer
Why: A petal is part of a flower; a page is part of a book (part and whole).
Find the odd one out: 27, 64, 125, 144, 216
- A) 64
- B) 125
- C) 216
- D) 144 ✔
Why: 144 is 12 squared, not a cube. The others are 3³, 4³, 5³ and 6³.
Carpenter : Saw :: Tailor : ?
- A) Needle ✔
- B) Cloth
- C) Shop
- D) Thread
Why: A saw is a carpenter's tool; a needle is a tailor's tool. Cloth and thread are materials, not tools.
What is your mother's brother called in Nepali?
- A) Kaka
- B) Mama ✔
- C) Phupu
- D) Thulobua
Why: Mother's brother is Mama (maternal uncle). Kaka and Thulobua are father's brothers; Phupu is father's sister.
What is your father's sister called in Nepali?
- A) Phupu ✔
- B) Sanima
- C) Maiju
- D) Kaki
Why: Father's sister is Phupu. Sanima is mother's younger sister and Maiju is Mama's wife.
What is your brother's son called?
- A) Cousin
- B) Grandson
- C) Nephew (Bhatija) ✔
- D) Brother-in-law
Why: A brother's son is a nephew, called Bhatija in Nepali.
Your son's wife is your:
- A) Sister-in-law
- B) Niece
- C) Cousin
- D) Daughter-in-law ✔
Why: A son's wife is a daughter-in-law (Buhari).
Who is your father's father's only son?
- A) Your father ✔
- B) Your uncle
- C) Your brother
- D) Your grandfather
Why: Your father's father is your grandfather; his only son is your father.
A is B's sister. C is B's mother. D is C's father. How is A related to D?
- A) Daughter
- B) Granddaughter ✔
- C) Niece
- D) Sister
Why: A is C's daughter, and C is D's child, so A is D's granddaughter.
Pointing to a man, Ram said, "His mother is the only daughter of my mother." How is the man related to Ram?
- A) Brother
- B) Cousin
- C) Nephew ✔
- D) Son
Why: The only daughter of Ram's mother is Ram's sister. The man is her son, so he is Ram's nephew (bhanja).
Introducing a woman, Hari said, "She is the wife of the only son of my father." How is the woman related to Hari?
- A) Sister
- B) Sister-in-law
- C) Mother
- D) Wife ✔
Why: The only son of Hari's father is Hari himself, so the woman is his wife.
P is the father of Q. R is the brother of P. How is R related to Q?
- A) Uncle ✔
- B) Brother
- C) Grandfather
- D) Cousin
Why: R is the brother of Q's father, so R is Q's paternal uncle (kaka or thulobua).
X is the brother of Y. Z is the father of X. W is the sister of Z. How is Y related to W?
- A) Son
- B) Brother
- C) Nephew or niece ✔
- D) Cousin
Why: Y is Z's child and W is Z's sister. Y's gender is not given, so Y is W's nephew or niece.
If A + B means A is the father of B and A × B means A is the brother of B, what does M + N × O tell us about M and O?
- A) M is O's brother
- B) M is O's father ✔
- C) M is O's uncle
- D) M is O's grandfather
Why: M is N's father and N is O's brother, so O is also M's child.
If A − B means A is the wife of B and A + B means A is the father of B, what is P in P − Q + R?
- A) R's sister
- B) R's mother ✔
- C) R's grandmother
- D) R's aunt
Why: P is Q's wife and Q is R's father, so P is R's mother.
Pointing to a girl, Sita said, "She is the daughter of my father's only son." How is the girl related to Sita?
- A) Daughter
- B) Sister
- C) Niece ✔
- D) Cousin
Why: Sita is a woman, so her father's only son is her brother. The girl is her brother's daughter, her niece (bhatiji).
Your mother's sister's son is your:
- A) Brother
- B) Nephew
- C) Uncle
- D) Cousin ✔
Why: The child of any aunt or uncle is a cousin.
A woman's husband's sister is her:
- A) Sister-in-law ✔
- B) Niece
- C) Aunt
- D) Cousin
Why: A husband's sister is a sister-in-law.
A is the wife of B, and B is the son of C. How is A related to C?
- A) Daughter
- B) Sister
- C) Daughter-in-law ✔
- D) Niece
Why: A is married to C's son, so A is C's daughter-in-law.
In Nepali, Kaka is your:
- A) Mother's brother
- B) Father's younger brother ✔
- C) Father's elder brother
- D) Sister's husband
Why: Kaka is the father's younger brother. The father's elder brother is Thulobua.
For a man, his sister's daughter is called:
- A) Bhatiji
- B) Buhari
- C) Bhanji ✔
- D) Phupu
Why: A sister's daughter is Bhanji. A brother's daughter is Bhatiji.
A and B are brothers. C is A's father. D is C's brother. E is D's son. How is B related to E?
- A) Brother
- B) Nephew
- C) Uncle
- D) Cousin ✔
Why: B's father C and E's father D are brothers, so B and E are cousins.
Pointing to a photograph, a man said, "Her father is the only son of my mother." Who is in the photograph?
- A) His daughter ✔
- B) His sister
- C) His niece
- D) His mother
Why: The only son of the man's mother is the man himself, so the girl's father is the man: she is his daughter.
You are facing North and turn right. Which direction are you facing now?
- A) West
- B) South
- C) East ✔
- D) North-East
Why: A right turn is 90° clockwise. Clockwise from North is East.
You are facing East and turn left twice. Which direction are you facing now?
- A) West ✔
- B) North
- C) South
- D) East
Why: Facing East, a left turn gives North; another left turn gives West.
You are facing South and turn right. Which direction are you facing now?
- A) East
- B) West ✔
- C) North
- D) South-East
Why: When you face South your right hand points West.
You are facing West and turn 90° clockwise. Which direction are you facing now?
- A) South
- B) East
- C) North ✔
- D) North-West
Why: Clockwise from West is North.
Which direction is opposite to North-East?
- A) North-West
- B) South-East
- C) South
- D) South-West ✔
Why: North-East and South-West are opposite directions.
You are facing North-West and turn 90° to the right. Which direction are you facing now?
- A) North-East ✔
- B) South-West
- C) South-East
- D) North
Why: 90° clockwise from North-West is North-East.
Ram walks 3 km North and then 4 km East. How far is he from the starting point?
- A) 7 km
- B) 1 km
- C) 5 km ✔
- D) 12 km
Why: Distance = √(3² + 4²) = √25 = 5 km.
Ram walks 3 km North and then 4 km East. In which direction is he from the starting point?
- A) North-West
- B) North-East ✔
- C) South-East
- D) East
Why: He is north and east of the start, so he is in the North-East direction.
A man walks 5 km North, turns right and walks 3 km, then turns right again and walks 5 km. Where is he from the start?
- A) 3 km West
- B) 13 km North
- C) 5 km East
- D) 3 km East ✔
Why: North 5 and South 5 cancel, leaving 3 km East.
In the morning, a man's shadow falls to his right. Which direction is he facing?
- A) South ✔
- B) North
- C) East
- D) West
Why: Morning shadows point West. If West is on his right, he is facing South.
In which direction does a shadow point in the evening?
- A) West
- B) North
- C) East ✔
- D) South
Why: In the evening the sun is in the West, so the shadow points East.
Sita is 7th from the left and 12th from the right in a row. How many people are in the row?
- A) 19
- B) 18 ✔
- C) 17
- D) 20
Why: Total = 7 + 12 − 1 = 18.
In a class of 40 students, Hari is 15th from the top. What is his rank from the bottom?
- A) 25th
- B) 24th
- C) 27th
- D) 26th ✔
Why: Rank from bottom = 40 − 15 + 1 = 26.
In a row of 30 people, A is 10th from the left and B is 15th from the right. How many people are between them?
- A) 5 ✔
- B) 4
- C) 6
- D) 7
Why: B is 30 − 15 + 1 = 16th from the left. Between them: 16 − 10 − 1 = 5.
A is 8th from the left and B is 12th from the right. They swap places, and A is now 15th from the left. How many people are in the row?
- A) 27
- B) 25
- C) 26 ✔
- D) 23
Why: A is in B's old place, which is 15th from the left and 12th from the right: 15 + 12 − 1 = 26.
Which formula gives the total number of people in a row?
- A) Left position + right position
- B) Left position + right position − 1 ✔
- C) Left position + right position + 1
- D) Left position × right position
Why: The person is counted from both ends, so subtract 1.
A girl walks 10 m South, turns left and walks 10 m, then turns left and walks 10 m. Where is she from the start?
- A) 10 m West
- B) 20 m South
- C) 10 m East ✔
- D) At the start
Why: Facing South, left is East; facing East, left is North. South and North cancel, leaving 10 m East.
You are facing South-East and turn back (180°). Which direction are you facing now?
- A) North-West ✔
- B) South-West
- C) North-East
- D) North
Why: The opposite of South-East is North-West.
Raju is 12th from the top and 20th from the bottom in his class. How many students are in the class?
- A) 32
- B) 30
- C) 33
- D) 31 ✔
Why: Total = 12 + 20 − 1 = 31.
In a queue, Gita is 5th from the front and Rita is 4 places behind Gita. What is Rita's position from the front?
- A) 8th
- B) 9th ✔
- C) 10th
- D) 1st
Why: 4 places behind 5th is 5 + 4 = 9th.
Which letter looks exactly the same in a mirror (left-right reflection)?
- A) B
- B) H ✔
- C) F
- D) R
Why: H has a vertical line of symmetry, so its mirror image is the same.
Which letter looks exactly the same in a water image (top-bottom reflection)?
- A) A
- B) M
- C) E ✔
- D) T
Why: E has a horizontal line of symmetry, so it looks the same upside-down in water.
Which letter looks the same in both a mirror image and a water image?
- A) O ✔
- B) A
- C) E
- D) M
Why: O is symmetric both left-right and top-bottom.
A mirror image swaps:
- A) Top and bottom
- B) Left and right ✔
- C) Both top-bottom and left-right
- D) Nothing
Why: A mirror at the side reverses left and right but keeps top and bottom.
A water image swaps:
- A) Left and right
- B) Nothing
- C) Top and bottom ✔
- D) The colour of the figure
Why: A reflection in water below the figure turns it upside down.
A clock seen in a mirror shows 3:15. What is the real time?
- A) 9:15
- B) 8:45 ✔
- C) 9:45
- D) 3:45
Why: Real time = 11:60 − 3:15 = 8:45.
A clock seen in a mirror shows 2:30. What is the real time?
- A) 9:30 ✔
- B) 10:30
- C) 8:30
- D) 2:30
Why: Real time = 11:60 − 2:30 = 9:30.
A square sheet is folded in half and then in half again, and one hole is punched. How many holes are there when it is opened?
- A) 2
- B) 3
- C) 8
- D) 4 ✔
Why: Two folds make 4 layers, and the punch goes through all of them.
A sheet is folded once and punched once. How many holes are there after opening?
- A) 1
- B) 2 ✔
- C) 3
- D) 4
Why: One fold makes 2 layers, so there are 2 holes.
A sheet is folded three times and punched once. How many holes are there after opening?
- A) 6
- B) 4
- C) 8 ✔
- D) 16
Why: Three folds make 2 × 2 × 2 = 8 layers.
On a standard die, which number is opposite 2?
- A) 5 ✔
- B) 4
- C) 6
- D) 3
Why: Opposite faces add up to 7, so 2 is opposite 5.
On a standard die, the numbers on opposite faces add up to:
- A) 6
- B) 8
- C) 7 ✔
- D) 12
Why: 1 and 6, 2 and 5, 3 and 4 are opposite pairs; each adds up to 7.
An arrow points up and turns 90° clockwise each step. Where does it point after 3 steps?
- A) Down
- B) Right
- C) Up
- D) Left ✔
Why: Up, then right, then down, then left after the third step.
A figure turns 45° each step. After how many steps does it return to its starting position?
- A) 4
- B) 8 ✔
- C) 6
- D) 12
Why: A full turn is 360°, and 360 ÷ 45 = 8.
In a triangle, lines from the top vertex divide the base into 4 parts. How many triangles are there in total?
- A) 10 ✔
- B) 8
- C) 4
- D) 12
Why: Triangles = n × (n + 1) ÷ 2 = 4 × 5 ÷ 2 = 10.
How many triangles are there in a square with both diagonals drawn?
- A) 4
- B) 6
- C) 8 ✔
- D) 10
Why: 4 small triangles and 4 larger triangles each made of two small ones.
How many squares are there in a 3 × 3 grid?
- A) 9
- B) 13
- C) 10
- D) 14 ✔
Why: 9 small squares, 4 squares of size 2 × 2 and 1 large square: 14.
How many squares are there in a 2 × 2 grid?
- A) 4
- B) 5 ✔
- C) 6
- D) 8
Why: 4 small squares and 1 large square.
Which word looks exactly the same in a mirror?
- A) BOB
- B) DAD
- C) MOM ✔
- D) NUN
Why: M and O are symmetric left to right and MOM reads the same backwards. B, D and N are not symmetric.
A dot starts at the top-left corner of a square and moves one corner clockwise each step. Where is it after 5 steps?
- A) Top-left
- B) Bottom-right
- C) Bottom-left
- D) Top-right ✔
Why: Top-right, bottom-right, bottom-left, top-left, then top-right on the fifth step.
What is the area of a rectangle 12 m long and 8 m wide?
- A) 40 m²
- B) 96 m² ✔
- C) 20 m²
- D) 84 m²
Why: Area = length × breadth = 12 × 8 = 96 m².
What is the perimeter of a rectangle 12 m long and 8 m wide?
- A) 40 m ✔
- B) 96 m
- C) 20 m
- D) 48 m
Why: Perimeter = 2(12 + 8) = 40 m.
What is the area of a square with side 9 cm?
- A) 36 cm²
- B) 18 cm²
- C) 81 cm² ✔
- D) 72 cm²
Why: Area = side² = 9 × 9 = 81 cm².
A square has a perimeter of 48 cm. What is its area?
- A) 144 cm² ✔
- B) 192 cm²
- C) 96 cm²
- D) 48 cm²
Why: Side = 48 ÷ 4 = 12 cm, so area = 12² = 144 cm².
What is the area of a circle with radius 7 cm?
- A) 44 cm²
- B) 49 cm²
- C) 308 cm²
- D) 154 cm² ✔
Why: Area = 22/7 × 7 × 7 = 154 cm².
What is the circumference of a circle with radius 7 cm?
- A) 22 cm
- B) 44 cm ✔
- C) 154 cm
- D) 14 cm
Why: Circumference = 2 × 22/7 × 7 = 44 cm.
What is the area of a triangle with base 10 cm and height 6 cm?
- A) 60 cm²
- B) 16 cm²
- C) 30 cm² ✔
- D) 32 cm²
Why: Area = ½ × 10 × 6 = 30 cm².
The two shorter sides of a right-angled triangle are 6 cm and 8 cm. How long is the hypotenuse?
- A) 10 cm ✔
- B) 14 cm
- C) 12 cm
- D) 9 cm
Why: √(6² + 8²) = √100 = 10 cm.
What is the volume of a cube with side 5 cm?
- A) 25 cm³
- B) 150 cm³
- C) 75 cm³
- D) 125 cm³ ✔
Why: Volume = 5³ = 125 cm³.
What is the total surface area of a cube with side 5 cm?
- A) 125 cm²
- B) 150 cm² ✔
- C) 100 cm²
- D) 25 cm²
Why: Total surface area = 6 × 5² = 150 cm².
What is the volume of a box 6 cm × 4 cm × 3 cm?
- A) 72 cm³ ✔
- B) 13 cm³
- C) 108 cm³
- D) 54 cm³
Why: Volume = 6 × 4 × 3 = 72 cm³.
What is the volume of a cylinder with radius 7 cm and height 10 cm?
- A) 440 cm³
- B) 154 cm³
- C) 1540 cm³ ✔
- D) 770 cm³
Why: Volume = 22/7 × 7 × 7 × 10 = 1540 cm³.
If the side of a square is doubled, its area becomes:
- A) 2 times
- B) 3 times
- C) 8 times
- D) 4 times ✔
Why: Area depends on side squared: 2² = 4.
1 cubic metre is equal to:
- A) 100 litres
- B) 1000 litres ✔
- C) 10 litres
- D) 10,000 litres
Why: 1 m³ = 1000 litres.
What is the area of the four walls of a room 5 m long, 4 m wide and 3 m high?
- A) 60 m²
- B) 27 m²
- C) 54 m² ✔
- D) 45 m²
Why: Area of four walls = 2 × height × (length + breadth) = 2 × 3 × 9 = 54 m².
In the Nepali hill land system, 1 ropani is equal to:
- A) 16 aana ✔
- B) 20 aana
- C) 4 aana
- D) 12 aana
Why: 1 ropani = 16 aana.
In the Terai land system, 1 bigha is equal to:
- A) 16 kattha
- B) 10 kattha
- C) 20 kattha ✔
- D) 25 kattha
Why: 1 bigha = 20 kattha.
In the Terai land system, 1 kattha is equal to:
- A) 16 dhur
- B) 20 dhur ✔
- C) 4 dhur
- D) 10 dhur
Why: 1 kattha = 20 dhur.
Which formula gives the volume of a sphere of radius r?
- A) 4πr²
- B) πr²h
- C) ⅓ πr²h
- D) ⁴⁄₃ πr³ ✔
Why: The volume of a sphere is four-thirds π r cubed; 4πr² is its surface area.
The circumference of a circle is 88 cm. What is its radius?
- A) 14 cm ✔
- B) 7 cm
- C) 28 cm
- D) 21 cm
Why: 2 × 22/7 × r = 88, so r = 88 × 7 ÷ 44 = 14 cm.