Question

# The ratio of the income to the expenditure of a family is $7:6$. Find the savings if the income of the family is Rs.42000?

Hint: First we’ll find the expenditure of the family using the ratio of the income to the expenditure of a family which is given in the question. Then using this we’ll find the savings of the family as the savings will be the difference in income and the expenditure of the family.

Given data: Ratio of income to the expenditure of a family is $7:6$
Income of family=Rs.42000
Let the expenditure of family be Rs.x
Therefore, according to the given data
i.e. $42000:x = 7:6$
$\Rightarrow \dfrac{{42000}}{x} = \dfrac{7}{6}$
After cross-multiplication, we get,
$\Rightarrow x = 42000\left( {\dfrac{6}{7}} \right)$
On further simplification we get,
$\Rightarrow x = 6000\left( 6 \right)$
$\therefore x = 36000$
Therefore, the expenditure of the family=Rs.36000
The savings of the family will be equal to the left amount out of the total income after the expenditure
i.e. Savings of the family=Income-Expenditure of the family
Savings of the family$= Rs.42000 - Rs.36000$
Therefore, Savings of the family$= Rs.6000$

Note: Ratio is always taken of the quantity having similar units, that is why a ratio is always a unitless quality.
In this question also we’ve given the ratio of income to expenditure since income and expenditure both are in rupees having the same unit hence the ratio will come out be a unitless value.