A money lender finds that due to fall in the annual rate of interset 8 % to `7 (3)/(4)` %, his yearly income diminishes by Rs 61.50. His capital is

Options

A. Rs 22400
B. Rs 23800
C. Rs 24600
D. Rs 26000

Answer

To solve the problem step by step, we will first determine the difference in interest rates and then calculate the capital based on the decrease in yearly income.

### Step 1: Identify the interest rates
The initial interest rate is 8%, and the new interest rate is \(7 \frac{3}{4}\%\).

### Step 2: Convert the mixed fraction to an improper fraction
To convert \(7 \frac{3}{4}\%\) to a decimal:
\[ 7 \frac{3}{4} = 7 + \frac{3}{4} = \frac{28}{4} + \frac{3}{4} = \frac{31}{4} = 7.75\% \]

### Step 3: Calculate the difference in interest rates
Now, we find the difference between the two interest rates:
\[ 8\% - 7.75\% = 0.25\% \]

### Step 4: Relate the difference in interest rates to the decrease in income
The problem states that this decrease in interest results in a loss of Rs 61.50 in yearly income. Therefore, we can set up the equation:
\[ 0.25\% \text{ of Capital} = 61.50 \]

### Step 5: Express the percentage as a fraction
We can express \(0.25\%\) as a fraction:
\[ 0.25\% = \frac{0.25}{100} = \frac{1}{400} \]

### Step 6: Set up the equation for Capital
Let \(C\) be the capital. Then we can write:
\[ \frac{1}{400} \times C = 61.50 \]

### Step 7: Solve for Capital
To find \(C\), multiply both sides by 400:
\[ C = 61.50 \times 400 \]
Calculating the right side:
\[ C = 24600 \]

### Final Answer
The capital is Rs 24,600.

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