A family spends 30% of its income on house rent and 60% of the rest on house hold expenses. If the total savings of the family is ₹ 12,600 per month, find the total monthly income of the family.

Given:

Percent of money the family spends on house rent = 30% of the salary

Remaining percent of money after paying house rent = (100% - 30%) = 70% of the salary

Let the salary of family be $x$.

Amount of money left after paying house rent = $\dfrac{70}{100} \times x$

= $\dfrac{7}{10} \times x$

= $\dfrac{7x}{10}$ ……….(1)

Percent of money the family spent on household expenses = 60% of the remaining amount

Left over money = (100% - 60%) = 40% of the remaining amount = 12,600.

$⇒ \dfrac{40}{100} \times \dfrac{7x}{10} = 12,600\\[1em] ⇒ \dfrac{2}{5} \times \dfrac{7x}{10} = 12,600\\[1em] ⇒ \dfrac{2 \times 7x}{5 \times 10} = 12,600\\[1em] ⇒ \dfrac{14x}{50} = 12,600\\[1em] ⇒ \dfrac{7x}{25} = 12,600\\[1em] ⇒ x = \dfrac{12,600 \times 25}{7}\\[1em] ⇒ x = \dfrac{3,15,00}{7}\\[1em] ⇒ x = 45,000$

Hence, the monthly income of the family = ₹ 45,000