Question

A person spends $80$% of his income. With the increase in the cost of living, his expenditure increases by $37\frac{1}{2}$% and his income increases by $16\frac{2}{3}$. His present percent saving is :__

• A. $6\frac{2}{3}$
• B. $5\frac{5}{7}$
• C. $20\frac{5}{6}$
• D. $13\frac{1}{3}$

Answer 1

The correct option is B $5\frac{5}{7}$

If the Income of the man is $I$ Expenditure $E=80$% of $I=0.8I$
Saving $S=I-E=0.2I$
Increased Income
$\frac{116\frac{2}{3}}{100}\times I=\frac{350}{300}I=70$
Increase expenditure
$=\frac{275}{200}\times \frac{4}{5}I=1.1I$
Saving $=\frac{350}{300}I-\frac{11}{10}I$
$=\frac{(350-330)I}{300}=\frac{20}{300}I$
Saving percent
$=\frac{20}{300}\times \frac{350}{300}\times 100$
$=\frac{40}{7}=5\frac{5}{7}$%