A man spends 75% of his monthly income, and his income increases by 10%. His expenditure also increases by 20%. By what percentage do his savings increase?
A) 10%
B) 20%
C) 30%
D) 50%Explain step by step 

Let's solve the problem step by step:

### Step 1: Initial situation
Let the man's initial monthly income be \( I \), and since he spends 75% of it, his expenditure is:
\[
\text{Expenditure} = 0.75I
\]
This means his initial savings are the remaining 25% of his income:
\[
\text{Savings} = 0.25I
\]

### Step 2: After the income increase
Now, the man's income increases by 10%. His new income becomes:
\[
\text{New Income} = I + 0.10I = 1.10I
\]

### Step 3: After the expenditure increase
The man's expenditure also increases, but by 20%. His new expenditure is 20% more than his original expenditure of \( 0.75I \):
\[
\text{New Expenditure} = 0.75I + 0.20 \times 0.75I = 0.75I + 0.15I = 0.90I
\]

### Step 4: New savings
His new savings will be the difference between his new income and new expenditure:
\[
\text{New Savings} = \text{New Income} - \text{New Expenditure} = 1.10I - 0.90I = 0.20I
\]

### Step 5: Percentage increase in savings
Initially, his savings were \( 0.25I \), and now they are \( 0.20I \). To find the percentage increase in savings, we use the formula for percentage increase:
\[
\text{Percentage increase} = \frac{\text{New Savings} - \text{Old Savings}}{\text{Old Savings}} \times 100
\]
Substituting the values:
\[
\text{Percentage increase} = \frac{0.20I - 0.25I}{0.25I} \times 100 = \frac{-0.05I}{0.25I} \times 100 = -20\%
\]

### Step 6: Conclusion
The savings actually **decrease by 20%**, not increase. However, this was not an option, which could suggest a clarification issue in the problem. However, based on the provided data, the correct interpretation shows a decrease.

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. What would happen if his expenditure increased by 10% instead of 20%?
2. How does the percentage increase in expenditure affect the overall savings change?
3. What is the formula for calculating percentage increase or decrease?
4. If his income increased by 15% but expenditure by only 5%, what would be the new percentage savings change?
5. How does the relationship between income and expenditure affect financial growth?

**Tip**: When dealing with percentage changes, always compare the change in savings to the initial values to ensure accurate results.

A man spends 75% of his monthly income, and his income increases by 10%. His expenditure also increases by 20%. By what percentage do his savings increase? A) 10% B) 20% C) 30% D) 50% Explain step by step.

Learn how to calculate the percentage change in savings when a man's income increases by 10% and his expenditure increases by 20%. This step-by-step solution involves key concepts such as percentage change, income and expenditure calculations, and savings analysis. Suitable for students in Grades 7-10.

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