Question

A man spends 80% of his income. His income increased by 25% and his expenditure increased by

10%. By how much did his savings increase?

Answer 1

Suppose earlier income of a man is x.
Earlier expenditure = 80% of income
This means earlier saving = $x-x\times \frac{80}{100}=x-\frac{4x}{5}=\frac{x}{5}$
Now, his income increased by 25%.
then present income = $x+x\times \frac{25}{100}=x+\frac{x}{4}=\frac{5x}{4}$
Now expenditure increased by 10%. this means his present expenditure is 90% of his present income.
So, present saving = $\frac{5x}{4}-\frac{5x}{4}\times \frac{90}{100}=\frac{5x}{4}-\frac{9x}{8}=\frac{x}{8}$
This means the present saving is less than earlier saving. so there is decrease in saving.
Net decrease = $\frac{x}{5}-\frac{x}{8}=\frac{3x}{40}$
So, net decrease percentage = $\frac{{\displaystyle \frac{3x}{40}}\times 100}{{\displaystyle \frac{x}{5}}}=\frac{3x}{40}\times \frac{5}{x}\times 100=\frac{75}{2}=37.5\%$
Therefore, there is decrease in savings instead of increase.