Ratio and Proportion: Note Quiz

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.

The simplest form of 45 : 60 is:

• A) 3 : 4 ✔
• B) 9 : 12
• C) 4 : 3
• D) 5 : 6

Why: Divide by 15.

The ratio of 50 paisa to Rs 2 is:

• A) 1 : 4 ✔
• B) 1 : 2
• C) 4 : 1
• D) 25 : 1

Why: 50 : 200.

Rs 1,500 is divided in the ratio 2 : 3. The larger share is:

• A) Rs 900 ✔
• B) Rs 600
• C) Rs 750
• D) Rs 1,000

Why: 3/5 × 1,500.

If A : B = 2 : 3 and B : C = 4 : 5, then A : B : C is:

• A) 8 : 12 : 15 ✔
• B) 2 : 3 : 5
• C) 4 : 6 : 5
• D) 8 : 10 : 15

Why: Make B equal (12).

The fourth proportional to 2, 3 and 4 is:

• A) 6 ✔
• B) 8
• C) 5
• D) 12

Why: 2 : 3 = 4 : x.

The third proportional to 4 and 6 is:

• A) 9 ✔
• B) 8
• C) 12
• D) 10

Why: 6² ÷ 4.

The mean proportional between 4 and 9 is:

• A) 6 ✔
• B) 6.5
• C) 13
• D) 36

Why: √36.

The duplicate ratio of 2 : 3 is:

• A) 4 : 9 ✔
• B) 8 : 27
• C) 2 : 3
• D) 3 : 2

Why: Squares.

The triplicate ratio of 1 : 2 is:

• A) 1 : 8 ✔
• B) 1 : 4
• C) 1 : 6
• D) 2 : 1

Why: Cubes.

The inverse ratio of 3 : 5 is:

• A) 5 : 3 ✔
• B) 3 : 5
• C) 9 : 25
• D) 1 : 15

Why: Reverse.

If x : 12 = 3 : 4, then x is:

• A) 9 ✔
• B) 16
• C) 8
• D) 6

Why: 12 × 3 ÷ 4.

If 3 : x = 9 : 15, then x is:

• A) 5 ✔
• B) 45
• C) 3
• D) 6

Why: 3 × 15 ÷ 9.

Two ages are in the ratio 3 : 5 and their sum is 40. The older person is:

• A) 25 ✔
• B) 15
• C) 20
• D) 30

Why: 5/8 × 40.

20 litres of mixture has milk and water 4 : 1. How much water must be added to make it 2 : 1?

• A) 4 litres ✔
• B) 8 litres
• C) 2 litres
• D) 5 litres

Why: Milk 16 needs water 8; add 4.

Two numbers are in the ratio 5 : 7 and their sum is 96. The smaller number is:

• A) 40 ✔
• B) 56
• C) 35
• D) 48

Why: 5/12 × 96.

Boys to girls in a class of 40 is 3 : 2. Number of girls:

• A) 16 ✔
• B) 24
• C) 20
• D) 15

Why: 2/5 × 40.

The compound ratio of 2 : 3 and 3 : 4 is:

• A) 1 : 2 ✔
• B) 6 : 7
• C) 5 : 7
• D) 2 : 1

Why: 6 : 12.

Two numbers are in the ratio 7 : 9 and differ by 8. The larger number is:

• A) 36 ✔
• B) 28
• C) 32
• D) 45

Why: 2 parts = 8.

The sub-triplicate ratio of 8 : 27 is:

• A) 2 : 3 ✔
• B) 4 : 9
• C) 8 : 27
• D) 3 : 2

Why: Cube roots.

If a : b = c : d, then:

• A) ad = bc ✔
• B) ab = cd
• C) ac = bd
• D) a + d = b + c

Why: Product of extremes = product of means.

For a fixed distance, speed and time are:

• A) Inversely proportional ✔
• B) Directly proportional
• C) Equal
• D) Unrelated

Why: More speed, less time.

Cost and quantity (at fixed price) are:

• A) Directly proportional ✔
• B) Inversely proportional
• C) Unrelated
• D) Equal

Why: More quantity, more cost.

A's and B's salaries are in the ratio 4 : 5. B gets Rs 25,000. A gets:

• A) Rs 20,000 ✔
• B) Rs 31,250
• C) Rs 18,000
• D) Rs 22,000

Why: 25,000 × 4/5.

The angles of a triangle are in the ratio 1 : 2 : 3. The largest angle is:

• A) 90° ✔
• B) 60°
• C) 120°
• D) 100°

Why: 3/6 × 180.

If a : b = 3 : 4, then (a + b) : b is:

• A) 7 : 4 ✔
• B) 4 : 7
• C) 3 : 7
• D) 7 : 3

Why: (3 + 4) : 4.