If the true discount due 2 years hence at 14% per annum be Rs 168. Find the sum due?

Options

A. Rs 768
B. Rs 720
C. Rs 700
D. Rs 750

Answer

To solve the problem, we need to find the sum due given the true discount, the rate of interest, and the time period. Here’s a step-by-step solution:

### Step 1: Understand the formula for True Discount
The formula for True Discount (TD) is given by:
\[ TD = \text{Present Worth (PW)} \times \frac{R \times T}{100} \]
Where:
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Rearrange the formula to find Present Worth (PW)
From the formula, we can rearrange it to find Present Worth:
\[ PW = \frac{TD \times 100}{R \times T} \]

### Step 3: Substitute the known values
Given:
- True Discount (TD) = Rs 168
- Rate (R) = 14%
- Time (T) = 2 years

Substituting these values into the formula:
\[ PW = \frac{168 \times 100}{14 \times 2} \]

### Step 4: Calculate Present Worth (PW)
Now, calculate the denominator:
\[ 14 \times 2 = 28 \]
Then calculate:
\[ PW = \frac{16800}{28} \]
Now perform the division:
\[ PW = 600 \]

### Step 5: Calculate the Sum Due
The Sum Due (S) can be calculated using the formula:
\[ S = PW + TD \]
Substituting the values we have:
\[ S = 600 + 168 \]
Now perform the addition:
\[ S = 768 \]

### Final Answer
The sum due is Rs 768.

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