The interest on a certain sum of money is Rs 22 and the true discount on the same sum for the same time and at the same rate is Rs 20. Find the sum.

Options

A. Rs 220
B. Rs 200
C. Rs 210
D. Rs 212

Answer

To solve the problem, we need to find the sum of money based on the given interest and true discount.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Interest (I) = Rs 22
- True Discount (TD) = Rs 20

2. **Use the Relationship Between Interest and True Discount:**
The relationship between interest (I), true discount (TD), and the sum (S) can be expressed as:
\[ I = \frac{TD \times I}{TD} \]
This means that the true discount is related to the interest and the sum.

3. **Calculate the Sum Using the Formula:**
We know that:
\[ S = \frac{I \times TD}{I - TD} \]
Substituting the values we have:
\[ S = \frac{22 \times 20}{22 - 20} \]

4. **Perform the Calculation:**
- Calculate the denominator:
\[ 22 - 20 = 2 \]
- Now substitute back into the equation:
\[ S = \frac{440}{2} = 220 \]

5. **Conclusion:**
The sum of money is Rs 220.

### Final Answer:
The sum is Rs 220.

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