Question

The ratio of milk and water in one pot is 3:5 and that in another pot is 6:1. In what ratio should the contents of the two pots be mixed as to make the ratio between milk and water 7:3?

• A. $\frac{22}{91}$
• B. $\frac{44}{91}$
• C. $\frac{88}{91}$
• D. $\frac{66}{91}$

Answer 1

The correct option is B

$\frac{44}{91}$

Let x litres of first mixture is taken
Quantity of milk =$\frac{3x}{8}l$
Quantity of water =$\frac{5x}{8}l$
Let y litres of second mixture is taken
Quantity of milk =$\frac{6y}{7}l$
Quantity of water =$\frac{y}{7}l$
After mixing both of the mixture,
quantity of milk= $(\frac{3x}{8}+\frac{6y}{7})l$
Quantity of water = $(\frac{5x}{8}+\frac{y}{7})I$

According to question,
$\frac{milk}{water}=\frac{7}{3}$

$\frac{\frac{3x}{8}+\frac{6y}{7}}{\frac{5x}{8}+\frac{y}{7}}=\frac{7}{3}$

$\frac{9x}{8}+\frac{18y}{7}=\frac{35x}{8}+\frac{7y}{7}$
$\frac{11y}{7}=\frac{26x}{8}$
$\frac{x}{y}=\frac{11\times 8}{26\times 7}=\frac{88}{182}=\frac{44}{91}$
Hence, correct answer is (B).