Suresh’s expenditure and savings are in the ratio of 3 : 1. His income increases by 25%. If his savings increase by 20%, then by how much percentage does his expenditure increase?

The correct option is 26 $\frac{2}{3}$%.

Let's break down the problem step-by-step:

Step 1: Understand the initial relationship between Income, Expenditure, and Savings
We know the fundamental formula:
Income = Expenditure + Savings
The ratio of Suresh's expenditure to his savings is given as 3 : 1.
Let Suresh's savings be $x$ and his expenditure be $3x$.
To make the calculations simple and avoid fractions initially, let's assume:
Savings = 100
Expenditure = 300
Therefore, his initial Income = Expenditure + Savings = 300 + 100 = 400.

Step 2: Calculate the new values after the percentage increases
1. Income Increase:
His income increases by 25%.
Increase in Income = 25% of 400 = $\frac{25}{100}\times 400=100$
New Income = 400 + 100 = 500.

2. Savings Increase:
His savings increase by 20%.
Increase in Savings = 20% of 100 = $\frac{20}{100}\times 100=20$
New Savings = 100 + 20 = 120.

Step 3: Find the new Expenditure
Using the formula: New Expenditure = New Income - New Savings
New Expenditure = 500 - 120 = 380.

Step 4: Calculate the percentage increase in Expenditure
Initial Expenditure = 300
New Expenditure = 380
Increase in Expenditure = 380 - 300 = 80
Percentage Increase in Expenditure = $\frac{\text{Increase}}{\text{Original Expenditure}}\times 100$
Percentage Increase = $\frac{80}{300}\times 100=\frac{80}{3}\%$
Converting $\frac{80}{3}$ to a mixed fraction:
$80÷3=26$ with a remainder of 2.
Therefore, the percentage increase in expenditure is 26 $\frac{2}{3}$%.