Rahul spends 70% of his income. His income increased by 15% and his expenditure increased by 7.5%. What is the percentage increase in his savings?

The correct option is 32.5%.

Let us solve the problem step-by-step by assuming a initial value for Rahul's income.

Step 1: Determine initial income, expenditure, and savings.

Let initial income = $100$

Rahul spends 70% of his income.

Initial expenditure = $70\%\text{of}100=70$

Initial savings = Income - Expenditure

$\text{Initial savings}=100-70=30$

Step 2: Calculate the new income, expenditure, and savings after the increases.

His income increases by 15%:

$\text{New Income}=100+(15\%\text{of}100)=100+15=115$

His expenditure increases by 7.5%:

$\text{Increase in expenditure}=7.5\%\text{of}70=\frac{7.5}{100}\times 70=5.25$

$\text{New Expenditure}=70+5.25=75.25$

Now, calculate the new savings:

$\text{New Savings}=\text{New Income}-\text{New Expenditure}$

$\text{New Savings}=115-75.25=39.75$

Step 3: Calculate the percentage increase in savings.

$\text{Increase in savings}=\text{New Savings}-\text{Initial Savings}=39.75-30=9.75$

$\text{Percentage increase in savings}=\left(\frac{\text{Increase in savings}}{\text{Initial Savings}}\right)\times 100$

$\text{Percentage increase}=\left(\frac{9.75}{30}\right)\times 100=\frac{975}{30}=32.5\%$

Hence, the percentage increase in his savings is 32.5%.