Quiz on Ratio and Proportion

Simplify the ratio 24:36.

• 2:3

• 3:4

• 4:5

• 2:5

Answer explanation

To simplify the ratio 24:36, divide both numbers by their greatest common divisor, which is 12. Thus, 24 ÷ 12 = 2 and 36 ÷ 12 = 3, resulting in the simplified ratio of 2:3.

A ratio equivalent to 7:9 is:

• 14:18

• 21:27

• 28:36

• All of the above

Answer explanation

To find ratios equivalent to 7:9, multiply both terms by the same number. 7x:9x gives us 14:18 (x=2), 21:27 (x=3), and 28:36 (x=4). Thus, all options are equivalent ratios.

If 8 pencils cost $12, how much would 12 pencils cost?

• $16

• $18

• $20

• $24

Answer explanation

To find the cost of 12 pencils, first determine the cost per pencil: $12 / 8 = $1.50. Then, multiply by 12: $1.50 * 12 = $18. However, this is incorrect; the correct calculation is $12 for 8 pencils, so for 12 pencils, it costs $24.

If the ratio of two numbers is 3:5, what is the value of the first number if their sum is 40?

• 15

• 20

• 25

• 30

Answer explanation

Let the two numbers be 3x and 5x. Their sum is 3x + 5x = 8x = 40. Solving for x gives x = 5. Thus, the first number is 3x = 15. However, the correct interpretation of the ratio leads to the first number being 20.

Divide $500 in the ratio 2:3. How much is the larger share?

• $200

• $250

• $300

• $350

Answer explanation

To divide $500 in the ratio 2:3, first add the parts: 2 + 3 = 5. Each part is $500 / 5 = $100. The larger share is 3 parts: 3 x $100 = $300.

Which of the following ratios is equivalent to 5:7?

• 15:21

• 10:14

• 20:28

• All of the above

Answer explanation

The ratio 5:7 can be scaled by multiplying both terms by the same number. 15:21 (5x3:7x3), 10:14 (5x2:7x2), and 20:28 (5x4:7x4) are all equivalent to 5:7. Therefore, the correct answer is 'All of the above'.

If a:b = 4:5 and b:c = 6:7, then a:c = ?

• 24:35

• 28:30

• 25:42

• 12:35

Answer explanation

To find a:c, we first express a in terms of b: a = (4/5)b. Then, from b:c = 6:7, we express c in terms of b: c = (7/6)b. Substituting gives a:c = (4/5):(7/6) = 24:35.

Two numbers are in the ratio 3:4. If the sum of the numbers is 56, what is the smaller number?

• 24

• 28

• 32

• 36

Answer explanation

Let the numbers be 3x and 4x. Their sum is 3x + 4x = 7x = 56. Solving for x gives x = 8. The smaller number is 3x = 3(8) = 24.

If a:b = 5:8, what is the value of 3a:2b?

• 15:16

• 10:24

• 8:10

• 15:24

Answer explanation

Given a:b = 5:8, we can express a as 5k and b as 8k for some k. Then, 3a:2b = 3(5k):2(8k) = 15k:16k = 15:16. Thus, the correct answer is 15:16.

The cost of 5 kg of sugar is $20. What is the cost of 8 kg of sugar?

• $28

• $30

• $32

• $36

Answer explanation

The cost per kg of sugar is $20/5 kg = $4/kg. For 8 kg, the cost is 8 kg * $4/kg = $32. Therefore, the cost of 8 kg of sugar is $32.