Question

Peter could save $10$% of his income. But two years later when his income is increased by $20$%, he could save the same amount only as before. By how much percent has his expenditure increased?

• A. $22$%
• B. $22\frac{2}{9}$%
• C. $23\frac{1}{3}$%
• D. $24$%

Answer 1

Answer: (B)

$22\frac{2}{9}$%

Let initial income of Peter be 'a'

Amount saved by Peter$=10$% of income

$=\frac{a}{10}$

Expenditure$=a-\frac{a}{10}=\frac{9a}{10}$

Increased income of Peter$=a+\frac{20}{100}a$

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

Savings after increase in income$=\frac{a}{10}$ (same as before)

$\therefore$ Expenditure$=\frac{6a}{5}-\frac{a}{10}$

$=\frac{11a}{10}$

Percentage increase in expenditure$=\frac{\frac{11a}{10}-\frac{9a}{10}}{\left(\frac{9a}{10}\right)}\times 100$

$=\frac{200}{9}$%$\approx 22.23$