The banker's gain of a certain sum due 2 years hence at `5%` per annum is Rs. 80. The present worth is -----

Options

A. 8000
B. 16000
C. 12000
D. 8800

Answer

To solve the problem, we need to find the present worth given the banker's gain, the rate of interest, and the time period. Let's break it down step by step.

### Step 1: Identify the given values
- Banker's Gain (BG) = Rs. 80
- Rate (R) = 5% per annum
- Time (T) = 2 years

### Step 2: Calculate the True Discount (TD)
The formula for True Discount is:
\[ TD = \frac{BG \times 100}{R \times T} \]

Substituting the values we have:
\[ TD = \frac{80 \times 100}{5 \times 2} \]
\[ TD = \frac{8000}{10} = 800 \]

### Step 3: Calculate the Present Worth (PW)
The formula for Present Worth is:
\[ PW = \frac{TD \times 100}{R \times T} \]

Now substituting the True Discount we calculated:
\[ PW = \frac{800 \times 100}{5 \times 2} \]
\[ PW = \frac{80000}{10} = 8000 \]

### Final Answer
The present worth is Rs. 8000.

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