Raman spends 80% of his income. If his income is increased b y 25% and the expenditure increases by 10%, then what will be the percentage increase in his savings?

Options

A. 17
B. 70
C. 77
D. 85

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine Initial Income and Expenditure
Let Raman's initial income be represented as \( I \). According to the problem, he spends 80% of his income. Therefore, his expenditure \( E \) can be calculated as:
\[ E = 0.8I \]
His savings \( S \) can be calculated as:
\[ S = I - E = I - 0.8I = 0.2I \]

### Step 2: Calculate New Income After Increase
Raman's income is increased by 25%. The new income \( I' \) can be calculated as:
\[ I' = I + 0.25I = 1.25I \]

### Step 3: Calculate New Expenditure After Increase
The expenditure is increased by 10%. The new expenditure \( E' \) can be calculated as:
\[ E' = E + 0.1E = 0.8I + 0.1(0.8I) = 0.8I + 0.08I = 0.88I \]

### Step 4: Calculate New Savings
Now, we can calculate the new savings \( S' \):
\[ S' = I' - E' = 1.25I - 0.88I = 0.37I \]

### Step 5: Calculate Increase in Savings
The increase in savings can be calculated as:
\[ \text{Increase in savings} = S' - S = 0.37I - 0.2I = 0.17I \]

### Step 6: Calculate Percentage Increase in Savings
To find the percentage increase in savings, we can use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in savings}}{S} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{0.17I}{0.2I} \right) \times 100 = \left( \frac{0.17}{0.2} \right) \times 100 = 85\% \]

### Conclusion
Thus, the percentage increase in Raman's savings is **85%**.

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