A man spends 75% of his income and saves the rest. If his income increases by 50% and spending increases by 80%, then what is the percentage change in his savings?

Options

A. 40% decrease
B. 20% increase
C. 50% decrease
D. 40% increase

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Determine the initial income, spending, and savings.

Let the initial income of the man be \( I = 100x \).

- His spending is 75% of his income:
\[ \text{Spending} = 75\% \times I = 0.75 \times 100x = 75x \]

- His savings are the remaining part of his income:
\[ \text{Savings} = I - \text{Spending} = 100x - 75x = 25x \]

### Step 2: Calculate the new income after a 50% increase.

If his income increases by 50%, the new income \( I' \) will be:
\[ I' = I + 0.50 \times I = 100x + 0.50 \times 100x = 100x + 50x = 150x \]

### Step 3: Calculate the new spending after an 80% increase.

If his spending increases by 80%, the new spending \( S' \) will be:
\[ S' = \text{Spending} + 0.80 \times \text{Spending} = 75x + 0.80 \times 75x = 75x + 60x = 135x \]

### Step 4: Calculate the new savings.

Now, we can calculate the new savings \( S' \):
\[ S' = I' - S' = 150x - 135x = 15x \]

### Step 5: Determine the change in savings.

The initial savings were \( 25x \) and the new savings are \( 15x \). The change in savings \( \Delta S \) is:
\[ \Delta S = S' - \text{Initial Savings} = 15x - 25x = -10x \]

### Step 6: Calculate the percentage change in savings.

The percentage change in savings is given by:
\[ \text{Percentage Change} = \left(\frac{\Delta S}{\text{Initial Savings}}\right) \times 100 = \left(\frac{-10x}{25x}\right) \times 100 = -40\% \]

### Final Answer:
The percentage change in his savings is \(-40\%\).

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