A person spends 60% of his monthly income. If his income increases by 60% and the expenditure increases by 90%, then what is the percentage increase or decrease in his monthly savings?

Options

A. Decrease by 25%
B. Decrease by 30%
C. Increase by 25%
D. Increase by 15%

Answer

Let's solve the problem step by step.

### Step 1: Define the Monthly Income and Expenditure
Let the monthly income of the person be \( I \). According to the problem, the person spends 60% of his income.

\[ \text{Expenditure} = 60\% \text{ of } I = 0.6I \]

### Step 2: Calculate Initial Savings
The savings can be calculated by subtracting the expenditure from the income.

\[ \text{Savings} = I - \text{Expenditure} = I - 0.6I = 0.4I \]

### Step 3: Calculate New Income After Increase
The income increases by 60%. Therefore, the new income \( I' \) is:

\[ I' = I + 60\% \text{ of } I = I + 0.6I = 1.6I \]

### Step 4: Calculate New Expenditure After Increase
The expenditure increases by 90%. Therefore, the new expenditure \( E' \) is:

\[ E' = \text{Expenditure} + 90\% \text{ of Expenditure} = 0.6I + 0.9 \times 0.6I = 0.6I + 0.54I = 1.14I \]

### Step 5: Calculate New Savings
Now, we can calculate the new savings \( S' \):

\[ S' = I' - E' = 1.6I - 1.14I = 0.46I \]

### Step 6: Calculate Change in Savings
Now we find the change in savings:

\[ \text{Change in Savings} = S' - S = 0.46I - 0.4I = 0.06I \]

### Step 7: Calculate Percentage Change in Savings
To find the percentage change in savings, we use the formula:

\[ \text{Percentage Change} = \left( \frac{\text{Change in Savings}}{\text{Initial Savings}} \right) \times 100 = \left( \frac{0.06I}{0.4I} \right) \times 100 \]

Simplifying this gives:

\[ \text{Percentage Change} = \left( \frac{0.06}{0.4} \right) \times 100 = 15\% \]

### Conclusion
The percentage increase in his monthly savings is **15%**.

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