QUESTION

CSAT

Hard

Maths

Prelims 2020

A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replace 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?

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Explanation

We are given a 20-litre bottle containing only liquid A initially. The process involves:

Removing 4 litres of liquid A.
Adding 4 litres of liquid B.
Repeating the above one more time.

Step 1: First Replacement

Amount of A before removal = 20 litres.
After removing 4 litres, remaining A = 16 litres.
Adding 4 litres of B, new mixture = 16 litres of A + 4 litres of B.

Step 2: Second Replacement

4 litres of this new mixture is removed. The proportion of A in the mixture is: $\frac{16}{20} = 0.8$
Amount of A removed = $0.8 \times 4 = 3.2$ litres.
Amount of B removed = $0.2 \times 4 = 0.8$ litres.

Remaining after removal: A = $16 - 3.2 = 12.8$ litres. B = $4 - 0.8 = 3.2$ litres. Adding back 4 litres of B, final mixture = 12.8 litres of A + 7.2 litres of B.