Question : The ratio of expenditure and savings of a person is 5 : 3. If the income increases by 20% and the expenditure increases by 10%, then the person's savings increase by:
Option 1: $36 \frac{2}{3}$%
Option 2: $3 \frac{1}{3}$%
Option 3: $13 \frac{2}{3}$%
Option 4: $30 \frac{1}{3}$%
Correct Answer: $36 \frac{2}{3}$%
Solution :
Given: The ratio of expenditure and savings = 5 : 3.
Income increases by 20% and expenditure increases by 10%.
Let the expenditure and savings be $5x$ and $3x$ respectively.
Income of person $= 5x + 3x = 8x$
The new income $=8x \times \frac{120}{100} = 9.6x$
New expenditure $=5x \times \frac{110}{100} = 5.5x$
New savings $=9.6x - 5.5x = 4.1x$
Savings increased by = $\frac{\text{change in savings}}{\text{initial savings}}\times100$
= $\frac{4.1x - 3x}{3x} \times 100 = 36 \frac{2}{3}$%
Hence, the correct answer is $36 \frac{2}{3}$%.
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