About this quiz
Fundamental Operations, BODMAS, Unitary Method, Fractions and Decimals: Solved Examples
This Lok Sewa practice set has 50 multiple-choice questions (Subject: Maths and IQ · For: Kharidar · 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 50 questions with answers and explanations
5 pens cost Rs 75. What do 8 pens cost?
- A) Rs 100
- B) Rs 120 ✔
- C) Rs 135
- D) Rs 150
Why: 1 pen = 15; 8 pens = 120.
6 men finish a job in 10 days. How many days will 15 men take?
- A) 4 ✔
- B) 5
- C) 6
- D) 25
Why: 6 × 10 = 60 man-days; 60 ÷ 15 = 4.
18 ÷ 3 × 2 + 4 − 1 = ?
- A) 15 ✔
- B) 3
- C) 13
- D) 2
Why: 6 × 2 = 12; 12 + 4 − 1 = 15.
2/3 + 1/4 = ?
- A) 3/7
- B) 11/12 ✔
- C) 5/12
- D) 1/2
Why: 8/12 + 3/12 = 11/12.
3/4 × 2/5 = ?
- A) 3/10 ✔
- B) 5/9
- C) 6/9
- D) 3/5
Why: Multiply the tops and bottoms: (3 × 2)/(4 × 5) = 6/20, which simplifies to 3/10.
3/4 ÷ 1/2 = ?
- A) 3/8
- B) 3/2 ✔
- C) 2/3
- D) 1/4
Why: 3/4 × 2 = 3/2.
0.125 as a fraction is:
- A) 1/4
- B) 1/8 ✔
- C) 1/5
- D) 1/6
Why: 0.125 = 125/1000. Dividing top and bottom by 125 gives 1/8.
2.5 × 0.4 = ?
- A) 0.1
- B) 1 ✔
- C) 10
- D) 0.01
Why: 25 × 4 = 100 with two decimal places = 1.00.
15% of 600 is:
- A) 60
- B) 75
- C) 90 ✔
- D) 150
Why: 15 × 600 ÷ 100 = 90.
Rs 1,200 divided in 2 : 3. The smaller share is:
- A) Rs 400
- B) Rs 480 ✔
- C) Rs 600
- D) Rs 720
Why: 1200 × 2/5 = 480.
3/5 as a percentage is:
- A) 35%
- B) 50%
- C) 60% ✔
- D) 65%
Why: 0.6 × 100 = 60%.
A car uses 16 L for 240 km. Litres needed for 360 km?
- A) 20
- B) 22
- C) 24 ✔
- D) 26
Why: 15 km per litre; 360 ÷ 15 = 24.
7 + 3 × (10 − 4) ÷ 2 = ?
- A) 16 ✔
- B) 30
- C) 13
- D) 25
Why: 3 × 6 ÷ 2 = 9; 7 + 9 = 16.
Which is the largest?
- A) 0.6
- B) 5/8 ✔
- C) 3/5
- D) 0.61
Why: Convert to decimals: 5/8 = 0.625 and 3/5 = 0.6. So 5/8 (0.625) is larger than 0.61, 0.6 and 3/5.
12 workers finish a job in 15 days. How many days for 20 workers?
- A) 8
- B) 9 ✔
- C) 10
- D) 25
Why: 12 × 15 = 180; 180 ÷ 20 = 9.
12 notebooks cost Rs 360. What do 5 notebooks cost?
- A) Rs 150 ✔
- B) Rs 180
- C) Rs 120
- D) Rs 160
Why: Unitary method: 1 notebook = 360 ÷ 12 = Rs 30, so 5 notebooks = 30 × 5 = Rs 150.
8 men build a wall in 12 days. How long will 16 men take?
- A) 6 days ✔
- B) 24 days
- C) 8 days
- D) 4 days
Why: More men means fewer days (inverse proportion). Total work = 8 × 12 = 96 man-days, so 16 men take 96 ÷ 16 = 6 days.
1 kg of apples costs Rs 240. What do 2.5 kg cost?
- A) Rs 600 ✔
- B) Rs 480
- C) Rs 650
- D) Rs 560
Why: Cost = 240 × 2.5 = 240 × 2 + 240 × 0.5 = 480 + 120 = Rs 600.
25 × 4 ÷ 5 + 3 = ?
- A) 23 ✔
- B) 20
- C) 25
- D) 17
Why: By BODMAS, do × and ÷ left to right first: 25 × 4 = 100, 100 ÷ 5 = 20, then 20 + 3 = 23.
100 − 4 × 5 + 10 ÷ 2 = ?
- A) 85 ✔
- B) 245
- C) 80
- D) 90
Why: Do × and ÷ first: 4 × 5 = 20 and 10 ÷ 2 = 5. Then 100 − 20 + 5 = 85.
(8 + 2) × (6 − 1) = ?
- A) 50 ✔
- B) 45
- C) 60
- D) 40
Why: Brackets first: 8 + 2 = 10 and 6 − 1 = 5. Then 10 × 5 = 50.
In BODMAS, the letter O stands for:
- A) Of (orders/powers) ✔
- B) Over
- C) Operation
- D) Odd
Why: BODMAS = Brackets, Of (also read as Orders, i.e. powers and roots), Division, Multiplication, Addition, Subtraction. 'Of' means multiply, as in 1/2 of 10.
1/2 + 1/3 = ?
- A) 5/6 ✔
- B) 2/5
- C) 1/6
- D) 2/3
Why: Use the LCM of 2 and 3, which is 6: 1/2 = 3/6 and 1/3 = 2/6. So 3/6 + 2/6 = 5/6.
5/6 − 1/3 = ?
- A) 1/2 ✔
- B) 4/3
- C) 2/3
- D) 1/6
Why: Change 1/3 to sixths: 1/3 = 2/6. Then 5/6 − 2/6 = 3/6 = 1/2.
2/5 of 15 = ?
- A) 6 ✔
- B) 5
- C) 3
- D) 7.5
Why: 'Of' means multiply: 15 × 2/5 = 30/5 = 6. Or find 1/5 of 15 = 3, then double it = 6.
7/8 ÷ 7/4 = ?
- A) 1/2 ✔
- B) 2
- C) 49/32
- D) 7/2
Why: To divide, multiply by the reciprocal: 7/8 × 4/7 = 28/56 = 1/2.
0.75 as a fraction is:
- A) 3/4 ✔
- B) 7/5
- C) 3/5
- D) 1/4
Why: 0.75 = 75/100. Divide top and bottom by 25: 3/4.
3/8 as a decimal is:
- A) 0.375 ✔
- B) 0.38
- C) 0.83
- D) 0.125
Why: Divide 3 by 8: 3 ÷ 8 = 0.375. Useful to remember: 1/8 = 0.125, so 3/8 = 3 × 0.125 = 0.375.
0.2 × 0.3 = ?
- A) 0.06 ✔
- B) 0.6
- C) 0.006
- D) 6
Why: Multiply as whole numbers: 2 × 3 = 6. There are two decimal places in total (one each), so the answer is 0.06.
4.5 ÷ 0.5 = ?
- A) 9 ✔
- B) 2.25
- C) 0.9
- D) 90
Why: Multiply both by 10 to remove decimals: 45 ÷ 5 = 9. Check: 0.5 × 9 = 4.5.
1.25 + 2.75 = ?
- A) 4 ✔
- B) 3.9
- C) 4.1
- D) 3
Why: Line up the decimal points: 1.25 + 2.75 = 4.00 = 4.
Which is the largest: 2/3, 3/4, 5/8, 7/12?
- A) 3/4 ✔
- B) 2/3
- C) 5/8
- D) 7/12
Why: As decimals: 2/3 ≈ 0.667, 3/4 = 0.75, 5/8 = 0.625, 7/12 ≈ 0.583. The largest is 3/4.
Which is the smallest: 1/2, 3/5, 4/9, 5/8?
- A) 4/9 ✔
- B) 1/2
- C) 3/5
- D) 5/8
Why: As decimals: 1/2 = 0.5, 3/5 = 0.6, 4/9 ≈ 0.444, 5/8 = 0.625. The smallest is 4/9.
The reciprocal of 3/7 is:
- A) 7/3 ✔
- B) 3/7
- C) −3/7
- D) 1/21
Why: The reciprocal flips numerator and denominator: 3/7 becomes 7/3. A number times its reciprocal is 1.
24/36 in simplest form is:
- A) 2/3 ✔
- B) 3/4
- C) 4/6
- D) 6/9
Why: The HCF of 24 and 36 is 12. Divide both by 12: 24/36 = 2/3.
17/5 as a mixed number is:
- A) 3 2/5 ✔
- B) 2 3/5
- C) 3 1/5
- D) 4 2/5
Why: 17 ÷ 5 = 3 with remainder 2, so 17/5 = 3 2/5.
2 1/4 as an improper fraction is:
- A) 9/4 ✔
- B) 7/4
- C) 6/4
- D) 11/4
Why: Multiply the whole number by the denominator and add the numerator: 2 × 4 + 1 = 9, so 2 1/4 = 9/4.
A tap fills 1/4 of a tank in 1 hour. How long to fill the whole tank?
- A) 4 hours ✔
- B) 2 hours
- C) 3 hours
- D) 1/4 hour
Why: 1 hour fills 1/4, so the whole tank (4/4) takes 4 × 1 = 4 hours.
A train covers 300 km in 5 hours. How far in 8 hours at the same speed?
- A) 480 km ✔
- B) 400 km
- C) 500 km
- D) 540 km
Why: Speed = 300 ÷ 5 = 60 km/h. In 8 hours: 60 × 8 = 480 km.
15 books cost Rs 600. How many books for Rs 1,000?
- A) 25 ✔
- B) 20
- C) 30
- D) 15
Why: 1 book = 600 ÷ 15 = Rs 40. Books for Rs 1,000 = 1,000 ÷ 40 = 25.
40 workers finish a job in 30 days. How long for 60 workers?
- A) 20 days ✔
- B) 45 days
- C) 25 days
- D) 15 days
Why: Inverse proportion: total work = 40 × 30 = 1,200 worker-days, so 60 workers take 1,200 ÷ 60 = 20 days.
Food lasts 100 soldiers for 30 days. How long for 150 soldiers?
- A) 20 days ✔
- B) 45 days
- C) 25 days
- D) 15 days
Why: Total food = 100 × 30 = 3,000 soldier-days. For 150 soldiers: 3,000 ÷ 150 = 20 days. More people means the food lasts fewer days.
1/4 of 1/2 of 800 = ?
- A) 100 ✔
- B) 200
- C) 400
- D) 50
Why: 1/2 of 800 = 400, and 1/4 of 400 = 100. Or 1/4 × 1/2 = 1/8, and 800 ÷ 8 = 100.
0.5% of 1,000 = ?
- A) 5 ✔
- B) 50
- C) 0.5
- D) 500
Why: 0.5% = 0.5/100 = 0.005. So 1,000 × 0.005 = 5. Shortcut: 1% of 1,000 is 10, so 0.5% is half of that, 5.
√144 = ?
- A) 12 ✔
- B) 14
- C) 11
- D) 16
Why: √144 = 12, because 12 × 12 = 144.
15² = ?
- A) 225 ✔
- B) 215
- C) 250
- D) 205
Why: 15² = 15 × 15 = 225. Shortcut for numbers ending in 5: 1 × 2 = 2, then write 25 → 225.
The cube root of 64 is:
- A) 4 ✔
- B) 8
- C) 6
- D) 16
Why: The cube root of 64 is 4, because 4 × 4 × 4 = 64.
999 + 99 + 9 = ?
- A) 1,107 ✔
- B) 1,097
- C) 1,117
- D) 1,007
Why: Think of each as one less than a round number: (1,000 − 1) + (100 − 1) + (10 − 1) = 1,110 − 3 = 1,107.
1,000 − 456 = ?
- A) 544 ✔
- B) 554
- C) 644
- D) 456
Why: 1,000 − 456 = 544. Check: 456 + 544 = 1,000.
36 × 25 = ?
- A) 900 ✔
- B) 800
- C) 925
- D) 1,000
Why: Multiplying by 25 is the same as × 100 ÷ 4: 36 × 100 = 3,600, and 3,600 ÷ 4 = 900.