# Q. A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

(a) 4:1

(b) 5:1

(c) 16:9

(d) 17: 8

Correct Answer: (c) 16:9

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation :**

## Replacement of Liquid A & B

After the first replacement, the bottle contains 16 litres of liquid A and 4 litres of liquid B. The ratio of liquid A to the total mixture is 16/20 = 4/5.

When 4 litres of the mixture is taken out again and replaced by liquid B, we can calculate how much liquid A was removed by multiplying the volume removed (4 litres) by the ratio of liquid A in the mixture (4/5). This gives us (4 * 4/5) = 3.2 litres of liquid A removed.

So after this second replacement, there are (16 – 3.2) = 12.8 litres of liquid A left in the bottle and (20 – 12.8) = 7.2 litres of liquid B.

The final ratio of liquid A to liquid B is therefore 12.8:7.2, which can be simplified to 16:9