If the true discount on a sum due 2 years hence at `5%` per annum be Rs. 75, then the sum due is-

Options

A. Rs. 750
B. Rs. 825
C. Rs. 875
D. Rs. 800

Answer

To solve the problem of finding the sum due when the true discount is given, we can follow these steps:

### Step 1: Understand the relationship between True Discount, Present Worth, and Sum Due
The formula for True Discount (TD) is given by:
\[ TD = \text{Sum Due} - \text{Present Worth} \]
Where:
- Sum Due (S) is the amount that is due in the future.
- Present Worth (PW) is the amount that would need to be invested today to equal the Sum Due at the end of the specified time period.

### Step 2: Calculate the Present Worth using the True Discount formula
We know:
- True Discount (TD) = Rs. 75
- Rate (R) = 5% per annum
- Time (T) = 2 years

Using the formula for Present Worth (PW):
\[ PW = \frac{TD}{\text{Rate} \times \text{Time}} \]
We can rearrange the formula to find the Present Worth:
\[ PW = \frac{75}{\frac{5}{100} \times 2} \]

### Step 3: Calculate the Present Worth
Now, substituting the values:
\[ PW = \frac{75}{0.05 \times 2} = \frac{75}{0.1} = 750 \]
So, the Present Worth (PW) is Rs. 750.

### Step 4: Calculate the Sum Due
Now that we have the Present Worth, we can find the Sum Due using the True Discount formula:
\[ S = PW + TD \]
Substituting the values:
\[ S = 750 + 75 = 825 \]

### Conclusion
Thus, the Sum Due is Rs. 825.

### Final Answer
The sum due is Rs. 825.

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