Question : A person saves $33 \frac{1}{3}\%$ of his income. If the savings increase by $22\%$ and the expenditure increases by $10\%$, then the percentage increase in his income is:
Option 1: 18%
Option 2: 14%
Option 3: 16%
Option 4: 22%
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Correct Answer: 14%
Solution :
Given:
Savings of the man = $33\tfrac{1}{3}\% = \frac{1}{3}$rd of income
Let the original income be $300x$
⇒ Original Savings = $100x$
So, Original Expenditure $=300x-100x = 200x$
According to the question,
New savings $=100x \times \frac{122}{100} = 122x$
New expenditure $=200x \times \frac{110}{100} = 220x$
The new income $=220x + 122x = 342x$
So, the percentage increase in income = $\frac{342x-300x}{300x}\times 100 =14\%$
Hence, the correct answer is 14%.
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