A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres 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 ✓ UPSC's answer
(d) 17 : 8

Why the answer is (c)

• Initial quantity of liquid A is 20 litres. After removing 4 litres and adding 4 litres of liquid B, the quantity of liquid A remaining is 20 - 4 = 16 litres.

• The concentration of liquid A in the mixture is now 16/20 = 4/5.

• In the second step, 4 litres of this mixture is removed. The amount of liquid A removed is 4 * (4/5) = 16/5 = 3.2 litres.

• The remaining quantity of liquid A is 16 - 3.2 = 12.8 litres.

• The total volume remains 20 litres, so the quantity of liquid B is 20 - 12.8 = 7.2 litres.

• The ratio of liquid A to liquid B is 12.8 : 7.2, which simplifies to 128 : 72, and further to 16 : 9.

Why the other options are wrong

(a) 4 : 1: This ratio (4:1) implies 16 litres of A and 4 litres of B, which would only be true if only one replacement step had occurred.
(b) 5 : 1: This ratio (5:1) implies 16.67 litres of A and 3.33 litres of B, which does not match the calculated quantities after two replacements.
(d) 17 : 8: This ratio (17:8) implies 13.6 litres of A and 6.4 litres of B, which is incorrect as the actual amount of A is 12.8 litres.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.