Ratio, Proportion
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The difference between the greatest and the smallest number is 36. The numbers areThree numbers are in the ratio 1 : 2 : 3 . 2 3 4
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Ratio of numbers = 1 : 2 : 3 . 2 3 4 = 1 × 12 : 2 × 12 : 3 × 12 2 3 4
= 6 : 8 : 9
Let the numbers be 6x, 8x and 9x.
Now, 9x – 6x = 36
⇒ x = 12
∴ Numbers are
72, 96 and 108.Correct Option: D
Ratio of numbers = 1 : 2 : 3 . 2 3 4 = 1 × 12 : 2 × 12 : 3 × 12 2 3 4
= 6 : 8 : 9
Let the numbers be 6x, 8x and 9x.
Now, 9x – 6x = 36
⇒ x = 12
∴ Numbers are
72, 96 and 108.
- Two numbers are in the ratio 2 : 3. If 2 is subtracted from the first and 2 is added to the second, the ratio becomes 1 : 2. The sum of the numbers is :
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Let the number be 2x and 3x.
Then.2x − 2 = 1 3x + 2 2
⇒ 4x – 4 = 3x + 2
∴ x = 6
∴ Sum of Sum of numbers = 5x
= 5 × 6 = 30Correct Option: A
Let the number be 2x and 3x.
Then.2x − 2 = 1 3x + 2 2
⇒ 4x – 4 = 3x + 2
∴ x = 6
∴ Sum of Sum of numbers = 5x
= 5 × 6 = 30
- Of the three numbers, the ratio of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400, then the second number is :
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Let the numbers be a, b and c.
Now, a : b = 8 : 9
b : c = 3 : 4
∴ a : b : c
= 8 × 3 : 9 × 3 : 9 × 4
= 24 : 27 : 36 = 8 : 9 : 12∴ a = b = c = k 8 9 12
⇒ a = 8k, b = 9k, c = 12k
According to the question,
8k × 12k = 2400⇒ k2 = 2400 = 25 8 × 12
⇒ k = 5
∴ Second number
= 9k = 9 × 5 = 45Correct Option: A
Let the numbers be a, b and c.
Now, a : b = 8 : 9
b : c = 3 : 4
∴ a : b : c
= 8 × 3 : 9 × 3 : 9 × 4
= 24 : 27 : 36 = 8 : 9 : 12∴ a = b = c = k 8 9 12
⇒ a = 8k, b = 9k, c = 12k
According to the question,
8k × 12k = 2400⇒ k2 = 2400 = 25 8 × 12
⇒ k = 5
∴ Second number
= 9k = 9 × 5 = 45
- In a 45 litres mixture of milk and water, the ratio of the milk to water is 2 : 1. When some quantity of water is added to the mixture, this ratio becomes 1 : 2. The quantity of water added is
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Quantity of milk in 45 litres = 2 × 45 = 30 litres. 3
∴ Water = (45 – 15)
= 15 litres
Let x litres of water be added.∴ 30 = 1 15 + x 2
⇒ 15 + x = 60
⇒ x = 60 – 15 = 45 litres.Correct Option: D
Quantity of milk in 45 litres = 2 × 45 = 30 litres. 3
∴ Water = (45 – 15)
= 15 litres
Let x litres of water be added.∴ 30 = 1 15 + x 2
⇒ 15 + x = 60
⇒ x = 60 – 15 = 45 litres.
- The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is
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Let the numbers be x, y and z. Then
x : y = 2 : 3 ; y : z = 5 : 8
∴ x : y : z = 2 × 5 : 3 × 5 : 3 × 8
= 10 : 15 : 24
Sum of the ratios
= 10 + 15 + 24 = 49∴ The second number = 15 × 45 = 30 49 Correct Option: C
Let the numbers be x, y and z. Then
x : y = 2 : 3 ; y : z = 5 : 8
∴ x : y : z = 2 × 5 : 3 × 5 : 3 × 8
= 10 : 15 : 24
Sum of the ratios
= 10 + 15 + 24 = 49∴ The second number = 15 × 45 = 30 49
