Ratio, Proportion
- A and B are two alloys of gold and copper prepared by mixing metals in the ratio 5 : 3 and 5 : 11 respectively. Equal quantities of these alloys are melted to form a third alloy C. The ratio of gold and copper in the alloy C is
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Let 1 kg of each of the alloys A and B be mixed together.
In alloy A,Quantity of gold = 5 kg. 8 Quantity of copper = 3 kg. 8
In alloy B,Quantity of gold = 5 kg. 16 Quantity of copper = 11 kg. 16 = 
5 + 5 
: 3 + 11 8 16 8 16 = 15 : 17 16 16
= 15 :17Correct Option: C
Let 1 kg of each of the alloys A and B be mixed together.
In alloy A,Quantity of gold = 5 kg. 8 Quantity of copper = 3 kg. 8
In alloy B,Quantity of gold = 5 kg. 16 Quantity of copper = 11 kg. 16 = 5 + 5 : 3 + 11 8 16 8 16 = 15 : 17 16 16
= 15 :17
- A mixture contains wine and water in the ratio 3 : 2 and another mixutre contains them in the ratio 4 : 5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of wine and water ?
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∴ Required ratio = 1 : 1 18 10
= 5 : 9= 3 : 9 × 3 = 3 : 5 2 5 5 ∴ 5 2 litre must be added 5 Correct Option: A
∴ Required ratio = 1 : 1 18 10
= 5 : 9= 3 : 9 × 3 = 3 : 5 2 5 5 ∴ 5 2 litre must be added 5
- Three vessels whose capacities are 3 : 2 : 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. Taking 1/3 of first, 1/2 of second and 1/7 of third mixtures, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is
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Let there be 3 litres, 2 litres and 1 litre of mixtures in three vessels respectively.
Vessel I
In 1 litre of mixture,Milk = 5 litre, water = 2 litre 7 7
Vessel II
In 1 litre of mixture,Milk = 4 litre, water = 1 litre 5 5
Vessel III
In 1/7 litre of mixture,Milk = 4 × 1 = 4 litre 5 7 35 Water = 1 litre 35
In new vessel,Mixture = 1 + 1 + 1 7 = 2 + 1 7 = 14 + 1 7 = 15 litres 7 Water = 2 + 1 = 1 7 5 35 = 10 + 7 + 1 = 18 litre 35 35
Required percentage= 18 × 100 35 15 7 = 18 × 7 × 100 = 24% 35 15 Correct Option: D
Let there be 3 litres, 2 litres and 1 litre of mixtures in three vessels respectively.
Vessel I
In 1 litre of mixture,Milk = 5 litre, water = 2 litre 7 7
Vessel II
In 1 litre of mixture,Milk = 4 litre, water = 1 litre 5 5
Vessel III
In 1/7 litre of mixture,Milk = 4 × 1 = 4 litre 5 7 35 Water = 1 litre 35
In new vessel,Mixture = 1 + 1 + 1 7 = 2 + 1 7 = 14 + 1 7 = 15 litres 7 Water = 2 + 1 = 1 7 5 35 = 10 + 7 + 1 = 18 litre 35 35
Required percentage= 18 × 100 35 15 7 = 18 × 7 × 100 = 24% 35 15
- The ratio of the quantities of an acid and water in a mixture is 1 : 3. If 5 litres of acid is further added to the mixture, the new ratio becomes 1 : 2. The quantity of new mixture (in litres) is
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Let the quantity of acid in original mixture be x litre and that of water be 3x litres.
∴ x + 5 = 1 3x 2
⇒ 2x + 10 = 3x
⇒ x = 10
∴ Quantity of new mixture
= 4x + 5 = 45 litresCorrect Option: D
Let the quantity of acid in original mixture be x litre and that of water be 3x litres.
∴ x + 5 = 1 3x 2
⇒ 2x + 10 = 3x
⇒ x = 10
∴ Quantity of new mixture
= 4x + 5 = 45 litres
- In a mixture of 25 litres, the ratio of acid to water is 4 : 1. Another 3 litres of water is added to the mixture. The ratio of acid to water in the new mixture is
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In 25 litres of mixture,
Acid = 4 × 25 = 20 litres 5
Water = 5 litres.
After adding 3 litres of water, quantity becomes 8 litres
∴ New ratio = 20 : 8 = 5 : 2Correct Option: A
In 25 litres of mixture,
Acid = 4 × 25 = 20 litres 5
Water = 5 litres.
After adding 3 litres of water, quantity becomes 8 litres
∴ New ratio = 20 : 8 = 5 : 2
