Question

The ratio in which two sugar solutions of the concentrations $15$ $\%$ and $40$ $\%$ are to be mixed to get a solution of concentration $30$ $\%$ is:

• A. $2:3$
• B. $3:2$
• C. $8:9$
• D. $9:8$

Answer 1

The correct option is A $2:3$

Let $a$ liters of the first solution and

$b$ liters of the second solution be taken.

$\frac{15a}{100}+\frac{40b}{100}=\frac{30}{100}(a+b)$

$15a+40b=30(a+b)$

Dividing by $5,$ we get

$3a+8b=6(a+b)$

$3a+8b=6a+6b$

$8b-6b=6a-3a$

$3a=2b$

$\frac{a}{b}=\frac{2}{3}$

$\therefore$ Required ratio $=2:3$