A person spends 75% of his income. If his income increases by 20% and expenses increase by 15% then find the per cent increase in his savings.

Given:

A person spends 75% of his income. His income increases by 20% and expenses increase by 15%.

To do:

We have to find the per cent increase in his savings.

Solutions:

Let the income of the person be $x$.

Expenditure of the person originally$=\frac{75}{100}x=\frac{3x}{4}$.

Savings of the person originally$=(100-75)\%=25\%$

$=\frac{25}{100}\times x$

$=\frac{x}{4}$

The new income of the person$=x+\frac{20}{100}x$

$=\frac{100x+20x}{100}$

$=\frac{120x}{100}$

$=\frac{6x}{5}$

New expenditure of the person$=\frac{3x}{4}+\frac{15}{100}\times\frac{3x}{4}$

$=\frac{3x}{4}+\frac{9x}{80}$

$=\frac{20(3x)+9x}{80}$

$=\frac{69x}{80}$

New savings of the person$=\frac{6x}{5}-\frac{69x}{80}$

$=\frac{16(6x)-69x}{80}$

$=\frac{96x-69x}{80}$

$=\frac{27x}{80}$

Percentage increase in savings$=\frac{\frac{27x}{80}-\frac{x}{4}}{\frac{x}{4}}\times100$%

$=\frac{\frac{27x-20x}{80}}{\frac{x}{4}}\times100$%

$=\frac{\frac{7x}{80}}{\frac{x}{4}}\times100$%

$=\frac{7}{20}\times100$%

$=7\times5$%

$=35\%$

The percentage increase in savings is 35%.

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Updated on: 10-Oct-2022

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