The monthly income of a person in the year 2020 was 65,000 and his monthly expenditure was 45,000. In the year 2021 his monthly income increased by 15% and his monthly expenditure by 7% What is the percentage increase in his savings?

The correct option is 33%.

To find the percentage increase in the person's savings, we can break down the calculation step-by-step:

Step 1: Calculate the savings in the year 2020
Savings are calculated as the difference between monthly income and monthly expenditure:

$$\text{Savings in 2020}=\text{Income in 2020}-\text{Expenditure in 2020}$$

Substituting the given values:

$$\text{Savings in 2020}=\mathrm{65,000}-\mathrm{45,000}=\mathrm{20,000}$$

Step 2: Calculate the changes in the year 2021
In 2021, the monthly income increased by 15% and the monthly expenditure increased by 7%.

First, calculate the increase in monthly income:

$$\text{Increase in Income}=15\%\text{of}\mathrm{65,000}=\frac{15}{100}\times \mathrm{65,000}=\mathrm{9,750}$$

Next, calculate the increase in monthly expenditure:

$$\text{Increase in Expenditure}=7\%\text{of}\mathrm{45,000}=\frac{7}{100}\times \mathrm{45,000}=\mathrm{3,150}$$

Step 3: Calculate the net increase in savings
The increase in savings is the difference between the increase in income and the increase in expenditure:

$$\text{Increase in Savings}=\text{Increase in Income}-\text{Increase in Expenditure}$$

Substituting the values:

$$\text{Increase in Savings}=\mathrm{9,750}-\mathrm{3,150}=\mathrm{6,600}$$

Step 4: Calculate the percentage increase in savings
Now, find the percentage increase relative to the savings in the year 2020:

$$\text{Percentage Increase}=\left(\frac{\text{Increase in Savings}}{\text{Savings in 2020}}\right)\times 100$$

Substituting the calculated values:

$$\text{Percentage Increase}=\left(\frac{\mathrm{6,600}}{\mathrm{20,000}}\right)\times 100=33\%$$

Therefore, the percentage increase in savings is 33%.