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1. A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?

A. 25 litres

B. 15 litres

C. 18 litres

D. 24 litres

Solution:

Let bucket contains 5x and 3x of liquids A and B respectively.
When 16 litres of mixture are drawn off, quantity of A in mixture left:
$\begin{aligned} 5 x - \frac{5}{8} \times 16 = 5 x - 10 \\ Similarly quantity of B in mixture left, \\ 3 x - \frac{3}{8} \times 16 = 3 x - 6 \\ Now the ratio becomes, \\ \frac{5 x - 10}{3 x - 6} = \frac{3}{5} \\ \Rightarrow 25 x - 50 = 9 x - 18 \\ \Rightarrow 16 x = 32 \\ \Rightarrow x = 2 \\ So, quantity of liquid B initially, \\ = 3 \times 2 = 6 litres \end{aligned}$

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