Find out the capital required to earn a monthly interest of Rs. 210 at 7 % simple interest.

Options

A. 18000
B. 24000
C. 30000
D. 36000

Answer

To find out the capital required to earn a monthly interest of Rs. 210 at 7% simple interest, we can use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} \]

### Step 1: Identify the known values
- Monthly interest (SI) = Rs. 210
- Rate (R) = 7%
- Time (T) = 1 month = \( \frac{1}{12} \) years

### Step 2: Substitute the known values into the formula
We need to find the Principal (P). Rearranging the formula gives:

\[ P = \frac{SI \times 100}{R \times T} \]

Substituting the known values:

\[ P = \frac{210 \times 100}{7 \times \frac{1}{12}} \]

### Step 3: Simplify the equation
Calculating the denominator first:

\[ R \times T = 7 \times \frac{1}{12} = \frac{7}{12} \]

Now substituting this back into the equation for P:

\[ P = \frac{210 \times 100}{\frac{7}{12}} \]

### Step 4: Multiply by the reciprocal
To divide by a fraction, multiply by its reciprocal:

\[ P = 210 \times 100 \times \frac{12}{7} \]

### Step 5: Calculate the values
Calculating \( 210 \times 100 = 21000 \):

\[ P = 21000 \times \frac{12}{7} \]

Now calculating \( \frac{12}{7} \):

\[ \frac{12}{7} \approx 1.714285714 \]

Now multiply:

\[ P = 21000 \times 1.714285714 \approx 36000 \]

### Final Answer
Thus, the capital required is Rs. 36,000.