Ratio, Proportion
- In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. To get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is
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Quantity of milk in 729 litres of mixture
= 7 × 729 = 567 litres 9
∴ Quantity of water
= (729 – 567) litres = 162 litres.
Let x litres of water is mixed to get the required ratio of 7 : 3∴ 567 = 7 162 + x 3
⇒ 7x + 1134 = 1701
⇒ 7x = 1701 – 1134 = 567⇒ x = 567 = 81 litres 7 Correct Option: A
Quantity of milk in 729 litres of mixture
= 7 × 729 = 567 litres 9
∴ Quantity of water
= (729 – 567) litres = 162 litres.
Let x litres of water is mixed to get the required ratio of 7 : 3∴ 567 = 7 162 + x 3
⇒ 7x + 1134 = 1701
⇒ 7x = 1701 – 1134 = 567⇒ x = 567 = 81 litres 7
- In 40 litres mixture of milk and water the ratio of milk to water is 7 : 1. In order to make the ratio of milk and water 3 : 1, the quantity of water (in litres) that should be added to the mixture will be
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In 40 litres mixture,
Quantity of milk= 7 × 40 = 35 litres 8
Quantity of water = 5 litres
Let x litres of water be mixed∴ 35 = 3 5 + x 1
⇒ 3x + 15 = 35
⇒ 3x = 20⇒ x = 20 = 6 2 litres 3 3 Correct Option: C
In 40 litres mixture,
Quantity of milk= 7 × 40 = 35 litres 8
Quantity of water = 5 litres
Let x litres of water be mixed∴ 35 = 3 5 + x 1
⇒ 3x + 15 = 35
⇒ 3x = 20⇒ x = 20 = 6 2 litres 3 3
- A jar contained a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar, this ratio became 2 : 3. The quantity of liquid A contained in the jar initially was
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Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.
After taking out 10 litres of the mixture,
Liquid A= 4x – 4 × 10 = (4x – 8) litres 5
Liquid B= 4x – 1 × 10 = (4x – 2) litres 5
After pouring 10 litres of liquid B,4x − 8 = 2 4x – 2 + 10 3
⇒ 12x – 24 = 8x + 16
⇒ 4x = 40⇒ x = 40 = 10 4
∴ Quantity of liquid A = 4x
= 4 × 10 = 40 litresCorrect Option: D
Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.
After taking out 10 litres of the mixture,
Liquid A= 4x – 4 × 10 = (4x – 8) litres 5
Liquid B= 4x – 1 × 10 = (4x – 2) litres 5
After pouring 10 litres of liquid B,4x − 8 = 2 4x – 2 + 10 3
⇒ 12x – 24 = 8x + 16
⇒ 4x = 40⇒ x = 40 = 10 4
∴ Quantity of liquid A = 4x
= 4 × 10 = 40 litres
- A jar contained a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar, this ratio became 2 : 3. The quantity of liquid A contained in the jar initially was
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Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.
After taking out 10 litres of the mixture,
Liquid A= 4x – 4 × 10 = (4x – 8) litres 5
Liquid B= 4x – 1 × 10 = (4x – 2) litres 5
After pouring 10 litres of liquid B,4x − 8 = 2 4x – 2 + 10 3
⇒ 12x – 24 = 8x + 16
⇒ 4x = 40⇒ x = 40 = 10 4
∴ Quantity of liquid A = 4x
= 4 × 10 = 40 litresCorrect Option: D
Let the initial quantity of liquids A and B in the jar be 4x and x litres respectively.
After taking out 10 litres of the mixture,
Liquid A= 4x – 4 × 10 = (4x – 8) litres 5
Liquid B= 4x – 1 × 10 = (4x – 2) litres 5
After pouring 10 litres of liquid B,4x − 8 = 2 4x – 2 + 10 3
⇒ 12x – 24 = 8x + 16
⇒ 4x = 40⇒ x = 40 = 10 4
∴ Quantity of liquid A = 4x
= 4 × 10 = 40 litres
- In a mixture of 75 litres, the ratio of milk to water is 2 : 1. The amount of water to be further added to the mixture so as to make the ratio of the milk to water 1 : 2 will be
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In 75 litres of the mixture,
Milk = 2 × 75 = 50 litres 3 Water = 1 × 75 = 25 litres 3
Let x litres of water be added.
Then,50 = 1 x + 25 2
⇒ x + 25 = 100
⇒ x = 75 litresCorrect Option: C
In 75 litres of the mixture,
Milk = 2 × 75 = 50 litres 3 Water = 1 × 75 = 25 litres 3
Let x litres of water be added.
Then,50 = 1 x + 25 2
⇒ x + 25 = 100
⇒ x = 75 litres
