Question 128

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Litres of liquid A contained by the can initially 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

$$\frac{A}{12y} = \frac{7y}{12y} (1- \frac{9}{12y})$$

A = 7/4 (4y-3)

B = 12y - 7y + 5.25 = 5y + 5.25

$$\frac{7/4 (4y-3)}{5y + 5.25} = \frac{7}{9}$$

y = 7/4

so volume = 12y = 21 ltr

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