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 step by step, we will use the relationship between Simple Interest (SI), True Discount (TD), and the Sum (Principal, P).

### Step 1: Understand the given information
- Simple Interest (SI) = Rs. 22
- True Discount (TD) = Rs. 20

### Step 2: Use the formula for Sum (P)
The formula relating the Sum (P), Simple Interest (SI), and True Discount (TD) is:
\[ P = \frac{SI \times TD}{SI - TD} \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values of SI and TD into the formula:
- SI = 22
- TD = 20

So, we have:
\[ P = \frac{22 \times 20}{22 - 20} \]

### Step 4: Calculate the denominator
First, calculate the denominator:
\[ 22 - 20 = 2 \]

### Step 5: Calculate the numerator
Now calculate the numerator:
\[ 22 \times 20 = 440 \]

### Step 6: Divide the numerator by the denominator
Now, divide the numerator by the denominator to find the sum:
\[ P = \frac{440}{2} = 220 \]

### Step 7: Conclusion
Thus, the sum (Principal) is Rs. 220.

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

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