A man pay 4 paise tax on one rupee if he finds that the rate of interest reduce from `4%` of `3.75%` then its income will decrease by `Rs. 48` then find its capital.

Options

A. `26,000`
B. `24,000`
C. `22,000`
D. `20,000`

Answer

To solve the problem, we need to find the capital based on the given information about the tax paid, the reduction in the rate of interest, and the decrease in income.

### Step 1: Understand the Tax Paid
The man pays 4 paise tax on 1 rupee. Since 1 rupee = 100 paise, the tax rate can be calculated as:
\[ \text{Tax Rate} = \frac{4 \text{ paise}}{100 \text{ paise}} = 0.04 \text{ or } 4\% \]

### Step 2: Determine the Change in Interest Rate
The interest rate is reduced from 4% to 3.75%. The change in interest rate can be calculated as:
\[ \text{Change in Interest Rate} = 4\% - 3.75\% = 0.25\% \]

### Step 3: Calculate the Decrease in Income
According to the problem, the decrease in income due to the change in interest rate is Rs. 48. This decrease can be expressed in terms of capital (C) and the change in interest rate:
\[ \text{Decrease in Income} = C \times \frac{\text{Change in Interest Rate}}{100} \]
Substituting the values we have:
\[ 48 = C \times \frac{0.25}{100} \]

### Step 4: Solve for Capital (C)
To find C, we rearrange the equation:
\[ C = \frac{48 \times 100}{0.25} \]
Calculating the right side:
\[ C = \frac{4800}{0.25} = 4800 \times 4 = 19200 \]

### Final Answer
The capital is Rs. 19200.

---