Question

A man spends 75% of his income This income is increased by 20% and he increases his expenditure by 10%. By what per cent are his savings increased ?

Answer 1

Let the initial income of the person is Rs. $x$

His expenditure is 75% of income, i.e. Rs. $\frac{3x}{4}$

His initial savings therefore become $x-\frac{3x}{4}=\frac{x}{4}$

Now, his new income can be written as $\frac{120}{100}\times x=Rs.\frac{6x}{5}$

New expenditure $=\frac{110}{100}\times \frac{3x}{4}=Rs.\frac{33x}{40}$

New savings $=\frac{6x}{5}-\frac{33x}{40}=\frac{15x}{40}=Rs.\frac{3x}{8}$

Percent increase in savings $=\frac{\frac{3x}{8}-\frac{x}{4}}{\frac{x}{4}}\times 100=\frac{4}{8}\times 100=50\%$