Ratio, Proportion
- 200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was
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Let the quantity of additional milk added = x litres
In the mixture of 200 litres,Quantity of milk = 17 × 200 20
= 170 litres
Quantity of water = 30 litres
According to the question,170 + x = 7 30 1
⇒ 170 + x = 210
⇒ x = 210 – 170
= 40 litresCorrect Option: B
Let the quantity of additional milk added = x litres
In the mixture of 200 litres,Quantity of milk = 17 × 200 20
= 170 litres
Quantity of water = 30 litres
According to the question,170 + x = 7 30 1
⇒ 170 + x = 210
⇒ x = 210 – 170
= 40 litres
- A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A
contained by the can initially was
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Let A = 7x litre, B = 5x litre
In 9 litres of mixture,A = 7x × 9 = 21 litres 12x 4 B = 5x × 9 = 15 litres 12x 4
In new situation,7x − 21 = 7/9 4 5x − 15 + 9 4 ⇒ 28x − 21 = 7 20x − 15 + 36 9
⇒ 252x – 189 = 140x + 147
⇒ 112x = 336 ⇒ x = 3
∴ Initial quantity of liquid A
= 7x = 7 × 3 = 21 litresCorrect Option: C
Let A = 7x litre, B = 5x litre
In 9 litres of mixture,A = 7x × 9 = 21 litres 12x 4 B = 5x × 9 = 15 litres 12x 4
In new situation,7x − 21 = 7/9 4 5x − 15 + 9 4 ⇒ 28x − 21 = 7 20x − 15 + 36 9
⇒ 252x – 189 = 140x + 147
⇒ 112x = 336 ⇒ x = 3
∴ Initial quantity of liquid A
= 7x = 7 × 3 = 21 litres
- A container contains two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with B, the ratio of A and B becomes 1:1. How many litres of liquid A was in the container initially ?
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Let Liquid A = 7x litres
Liquid B = 5x litres
In 9 litres,A = 7 × 9 = 21 litres 12 4 B = 5 × 9 = 15 litres 12 4 ∴ 7x − 21 = 5x − 15 + 9 4 4 ⇒ 2x = 21 − 15 + 9 4 4 ⇒ 2x = 21 − 15 + 36 = 42 4 4 ⇒ x = 21 4 ∴ Liquid A = 7 × 21 4 = 147 = 36 3 litre 4 4 Correct Option: C
Let Liquid A = 7x litres
Liquid B = 5x litres
In 9 litres,A = 7 × 9 = 21 litres 12 4 B = 5 × 9 = 15 litres 12 4 ∴ 7x − 21 = 5x − 15 + 9 4 4 ⇒ 2x = 21 − 15 + 9 4 4 ⇒ 2x = 21 − 15 + 36 = 42 4 4 ⇒ x = 21 4 ∴ Liquid A = 7 × 21 4 = 147 = 36 3 litre 4 4
- A and B are two alloys of gold and copper prepared by mixing metals in ratios 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be ;
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Gold = 7 : 7 = 14 : 7 9 18 18 18
∴ Gold in new mixture
= 14 + 7 = 21
and copper = 18 × 2 – 21
= 36 – 21 = 15
∴ Required ratio
= 21 : 15 = 7 : 5Correct Option: A
Gold = 7 : 7 = 14 : 7 9 18 18 18
∴ Gold in new mixture
= 14 + 7 = 21
and copper = 18 × 2 – 21
= 36 – 21 = 15
∴ Required ratio
= 21 : 15 = 7 : 5
- The ratio in which a man must mix rice at 10.20 per kg and 14.40 per kg so as to make a
mixture worth 12.60 per kg, is
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∴ Required ratio = 1.8 : 2.4
= 18 : 24 = 3 : 4Correct Option: D
∴ Required ratio = 1.8 : 2.4
= 18 : 24 = 3 : 4
