Ratio, Proportion
- A mixture of 30 litres contain milk and water in the ratio of 7 : 3. How much water should be added to it so that the ratio of milk and water becomes 3 : 7 ?
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Quantity of milk in 30 litre mixture
= 30 × 7 = 21 litres 10
Quantity of water= 30 × 3 = 9 litres 10
Suppose x litres more water is added.
According to question,21 = 3 9 + x 7
⇒ 9 + x = 49
⇒ x = 40 litresCorrect Option: A
Quantity of milk in 30 litre mixture
= 30 × 7 = 21 litres 10
Quantity of water= 30 × 3 = 9 litres 10
Suppose x litres more water is added.
According to question,21 = 3 9 + x 7
⇒ 9 + x = 49
⇒ x = 40 litres
- A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?
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Let the barrel contain 4 litres of mixture.
∴ Wine = 3 litres
Water = 1 litre
Let x litre mixture is taken out.
∴ Wine in (4 – x) litres mixture= 3 (4 − x) 4
On adding x litres water, water in mixture= (4 − x) × 1 + x 4 = 1 − x + x 4 = 4 − x + 4x = 4 + 3x 4 4 ∴ 3 (4 − x) = 4 + 3x 4 4 ⇒ 3 − 3x = 1 + 3x 4 4 ⇒ 2 = 6x 4 ⇒ x = 2 × 4 = 4 6 3 ∴ Required answer = (4/3) = 1 4 3 Correct Option: B
Let the barrel contain 4 litres of mixture.
∴ Wine = 3 litres
Water = 1 litre
Let x litre mixture is taken out.
∴ Wine in (4 – x) litres mixture= 3 (4 − x) 4
On adding x litres water, water in mixture= (4 − x) × 1 + x 4 = 1 − x + x 4 = 4 − x + 4x = 4 + 3x 4 4 ∴ 3 (4 − x) = 4 + 3x 4 4 ⇒ 3 − 3x = 1 + 3x 4 4 ⇒ 2 = 6x 4 ⇒ x = 2 × 4 = 4 6 3 ∴ Required answer = (4/3) = 1 4 3
- There is 81 litres pure milk in a container. One-third of milk is replaced by water in the container. Again one-third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?
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Quantity of milk in the last
= 81 
1 − 27 
2 = 81 1 − 1 2 81 3 = 81 × 2 × 2 = 36 3 3
Quantity of water in the last
= 81 – 36 = 45∴ Ratio = 36 × 4 = 4 : 5 45 5 Correct Option: D
Quantity of milk in the last
= 81 1 − 27 2 = 81 1 − 1 2 81 3 = 81 × 2 × 2 = 36 3 3
Quantity of water in the last
= 81 – 36 = 45∴ Ratio = 36 × 4 = 4 : 5 45 5
- What number should be subtracted from both the terms of the ratio 11 : 15 so as to make it as 2 : 3 ?
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Required number = x
∴ 11 − x = 2 15 − x 3
⇒ 33 – 3x = 30 – 2x
⇒ 3x – 2x = 33 – 30
⇒ x = 3Correct Option: B
Required number = x
∴ 11 − x = 2 15 − x 3
⇒ 33 – 3x = 30 – 2x
⇒ 3x – 2x = 33 – 30
⇒ x = 3
- The ratio between two numbers is 2 : 3. If each number is increased by 4, the ratio between
them becomes 5 : 7. The difference between the numbers is
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Let the numbers be 2x and 3x.
∴ 2x + 4 = 5 3x + 4 7
∴ 15x + 20 = 14x + 28
⇒ x = 28 – 20 = 8
= Required difference
Second Method :
Here, a = 2, b = 3,c = 5, d = 7 and x = 41st Number = xa(c − d) ad − bc = 4 × 2(5 − 7) 2 × 7 − 5 × 3 = 8 × −2 = 16 14 − 15 2nd Number = xa(c − d) ad − bc = 4 × 3(5 − 7) 2 × 7 − 5 × 3 = 4 × 3 (−2) = 24 14 − 15
Difference of numbers
= 24 – 16 = 8Correct Option: A
Let the numbers be 2x and 3x.
∴ 2x + 4 = 5 3x + 4 7
∴ 15x + 20 = 14x + 28
⇒ x = 28 – 20 = 8
= Required difference
Second Method :
Here, a = 2, b = 3,c = 5, d = 7 and x = 41st Number = xa(c − d) ad − bc = 4 × 2(5 − 7) 2 × 7 − 5 × 3 = 8 × −2 = 16 14 − 15 2nd Number = xa(c − d) ad − bc = 4 × 3(5 − 7) 2 × 7 − 5 × 3 = 4 × 3 (−2) = 24 14 − 15
Difference of numbers
= 24 – 16 = 8
