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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%.