Ratio, Proportion
- 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
- 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
- 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
- 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
- 60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is
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In 60 kg of alloy A,
Lead = 3 × 60 = 36 kg. 5 Tin = 2 × 60 = 24 kg. 5
In 100 kg of alloy B,Tin = 1 × 100 = 20 kg. 5
In 160 kg of new alloy,
Tin = 24 + 20 = 44 kg.Correct Option: B
In 60 kg of alloy A,
Lead = 3 × 60 = 36 kg. 5 Tin = 2 × 60 = 24 kg. 5
In 100 kg of alloy B,Tin = 1 × 100 = 20 kg. 5
In 160 kg of new alloy,
Tin = 24 + 20 = 44 kg.
