### A can contains a mixture of two liquids A and B is 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. How many litres of liquid A was contained by the can initially?

A. 10 B. 20 C. 21 D. 25 Answer: Option C

### Solution(By Apex Team)

\begin{array}{l}\text{Suppose the can initially contains}\\ \text{7x and 5x of mixtures A and B respectively}\\ \text{Quantity of A in mixture left}\\ \begin{aligned}&=\left(7x-\frac{7}{12}\times9\right)\text{ litres }\\ &=\left(7x-\frac{21}{4}\right)\text{ litres }\\ &\text{ Quantity of B in mixture left }\\ &=\left(5x-\frac{5}{12}\times9\right)\text{ litres }\\ &=\left(5x-\frac{15}{4}\right)\text{ litres }\\ &\therefore\frac{\left(7x-\frac{21}{4}\right)}{\left(5x-\frac{15}{4}\right)+9}=\frac{7}{9}\\ &\Rightarrow\frac{28x-21}{20x+21}=\frac{7}{9}\\ &\Rightarrow252x-189=140x+147\\ &\Rightarrow112x=336\\ &\Rightarrow x=3\end{aligned}\end{array} So, the can contained 21 litres of A

## Related Questions On Alligation

A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2

### An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres