Ratio, Proportion
- Three glasses of equal volume contains acid mixed with water. The ratios of acid and water are 2 : 3, 3 : 4 and 4 : 5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water in the large vessel is
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Let the capacity of each glass be 1 litre.
On mixing all three mixtures together,Acid ⇒ 2 + 3 + 4 5 7 9 = 126 + 135 + 140 315 = 401 litre 315 Water ⇒ 3 + 4 + 5 5 7 9 = 189 + 180 + 175 = 544 315 315 ∴ Required ratio = 401 : 544 315 315 Correct Option: B
Let the capacity of each glass be 1 litre.
On mixing all three mixtures together,Acid ⇒ 2 + 3 + 4 5 7 9 = 126 + 135 + 140 315 = 401 litre 315 Water ⇒ 3 + 4 + 5 5 7 9 = 189 + 180 + 175 = 544 315 315 ∴ Required ratio = 401 : 544 315 315
- Two blends of a commodity costing Rs. 35 and Rs. 40 per kg. respectively are mixed in the ratio 2 : 3 by weight. If one–fifth of the mixture is sold at Rs. 46 per kg and the remaining at the
rate of Rs. 55 per kg. the profit percent is
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Let 5 kg of mixture be prepared.
∴ C.P. of 5 kg of mixture
= Rs. (2 × 35 + 3 × 40)
= Rs. (70 + 120)
= Rs. 190
Total S.P. of this mixture
= Rs. (46 + 4 × 55)
= Rs. (46 + 220) = Rs. 266
∴ Profit per cent= 
266 − 190 
× 100 190 = 7600 = 40% 190 Correct Option: C
Let 5 kg of mixture be prepared.
∴ C.P. of 5 kg of mixture
= Rs. (2 × 35 + 3 × 40)
= Rs. (70 + 120)
= Rs. 190
Total S.P. of this mixture
= Rs. (46 + 4 × 55)
= Rs. (46 + 220) = Rs. 266
∴ Profit per cent= 266 − 190 × 100 190 = 7600 = 40% 190
- 20 litres of a mixture contains milk and water in the ratio 3 : 1. Then the amount of milk to be added to the mixture so as to have milk and water in ratio 4 : 1 is :
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In 20 litres of mixture,
Milk ⇒ 3 × 20 = 15 litres 4 Water ⇒ 1 × 20 = 5 litres 4
Let the quantity of milk added be x litres.
According to the question,15 + x = 4 5 1
⇒ 15 + x = 4 × 5
⇒ x = 20 – 15 = 5 litresCorrect Option: C
In 20 litres of mixture,
Milk ⇒ 3 × 20 = 15 litres 4 Water ⇒ 1 × 20 = 5 litres 4
Let the quantity of milk added be x litres.
According to the question,15 + x = 4 5 1
⇒ 15 + x = 4 × 5
⇒ x = 20 – 15 = 5 litres
- A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is :
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Quantity of milk in the mixture = 5x litres
Quantity of water = x litres
According to the question,
On adding 5 litres of water,5x = 5 x + 5 2
⇒ 10x = 5x + 25
⇒ 5x = 25 ⇒ x = 5
∴ Required quantity of milk
= 5 × 5 = 25 litresCorrect Option: A
Quantity of milk in the mixture = 5x litres
Quantity of water = x litres
According to the question,
On adding 5 litres of water,5x = 5 x + 5 2
⇒ 10x = 5x + 25
⇒ 5x = 25 ⇒ x = 5
∴ Required quantity of milk
= 5 × 5 = 25 litres
- A vessel contains 60 litres of milk. 12 litres of milk is taken out from it and replaced by water. Then again from mixture, 12 litres is again taken out and replaced by water. The ratio of milk and water in the resultant mixture is :
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Remaining amount of milk = Initial quantity
= 1 − quantity taken out n Initial quantity = 60 1 − 12 2 60 = 60 1 − 1 2 5 = 60 × 4 × 4 5 5
= 38.4 litres
Quantity of water = 60 – 38.4
= 21.6 litres
∴ Required ratio
= 38.4 : 21.6 = 16 : 9Correct Option: B
Remaining amount of milk = Initial quantity
= 1 − quantity taken out n Initial quantity = 60 1 − 12 2 60 = 60 1 − 1 2 5 = 60 × 4 × 4 5 5
= 38.4 litres
Quantity of water = 60 – 38.4
= 21.6 litres
∴ Required ratio
= 38.4 : 21.6 = 16 : 9
