Question 110

A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litre of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was:

Solution

$$\frac{QNR}{total} = \frac{QNR(initial)}{total} (1- \frac{\textrm{Replaced Quantity}}{total})$$

QNR is the quantity which has not entered again

so here QNR is A

$$\frac{A}{5x} = \frac{4x}{5x} (1- \frac{10}{5x})$$

A = 4(x- 2)

B = 5x - 4x + 8 = x+3

$$\frac{4x-8}{x+3} = \frac{2}{3}$$

12x - 24 = 2x + 6

10 x = 30

x = 3

so volume = 5x = 5 x 3 = 15 ltr

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