question_answer

Two vessels A and B contain milk and water mixed in the ratio 8: 5 and 5: 2, respectively. The ratio in which these two mixtures be mixed to get a new mixture containing \[69\frac{3}{13}%\] milk is,

A) 2 : 7     

B) 3 : 5

C) 5 : 2                             

D) 5 : 7

Correct Answer: A

Solution :

Let cost of 1 L milk be Rs. 1.

Milk in 1 L mixture in \[A=Rs.\frac{8}{13}L,\]

CP of 1 L mixture in \[A=Rs.\,\frac{8}{13}\]

Milk in 1 L mixture in \[B=\frac{5}{7}L,\]

CP of 1 L mixture in \[B=Rs.\,\frac{5}{7}\]

Milk in 1 L of final mixture

\[=\left( \frac{900}{13}\times \frac{1}{100}\times 1 \right)=\frac{9}{13}L\]

Mean price \[=Rs.\,\,\frac{9}{13}\]

By the rule of alligation, we have

\[\therefore \] Required ratio \[=\frac{2}{91}:\frac{1}{13}=2:7\]