Ratio, Proportion
- 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
- The sum of three numbers is 116. The ratio of second to the third is 9 : 16 and the first to
the third is 1 : 4. The second number is
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Therefore, second number= 9 × 116 = 9 × 116 9 + 16 + 4 29
= 36Correct Option: D
Therefore, second number= 9 × 116 = 9 × 116 9 + 16 + 4 29
= 36
- Three numbers are in the ratio of 3 : 2 : 5 and the sum of their squares is 1862. The smallest of these numbers is
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Let the numbers be 3x, 2x
and 5x respectively.
Now, (3x)2 + (2x)2 + (5x)2
= 1862
⇒ 9x2 + 4x2 + 25x2 = 1862
⇒ 38x2 = 1862⇒ x2 = 1862 = 49 38
⇒ x = √49 = 7
∴ The smallest number
= 2x = 2 × 7 = 14Correct Option: C
Let the numbers be 3x, 2x
and 5x respectively.
Now, (3x)2 + (2x)2 + (5x)2
= 1862
⇒ 9x2 + 4x2 + 25x2 = 1862
⇒ 38x2 = 1862⇒ x2 = 1862 = 49 38
⇒ x = √49 = 7
∴ The smallest number
= 2x = 2 × 7 = 14
- The product of two positive integers is 1575 and their ratio is 9 : 7. The smaller integer is
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Let the integers be 9x and 7x respectively.
According to the question,
9x × 7x = 1575⇒ x2 = 1575 63
⇒ x2 = 25
⇒ x = 5
[x being positive (+ve) integer]
∴ Smaller integer
= 7x = 7 × 5 = 35Correct Option: B
Let the integers be 9x and 7x respectively.
According to the question,
9x × 7x = 1575⇒ x2 = 1575 63
⇒ x2 = 25
⇒ x = 5
[x being positive (+ve) integer]
∴ Smaller integer
= 7x = 7 × 5 = 35