The banker's gain of a sum due 8 yr, hence at 24 % per annum, is X 144. Find the present worth of that bill.

Options

A. 1) 39.06
B. 2) 45
C. 3) 38.06
D. 4) 50

Answer

To find the present worth of a bill given the banker's gain, we can follow these steps:

### Step 1: Understand the Given Information
- Banker's Gain (BG) = ₹144
- Rate (r) = 24% per annum
- Time (t) = 8 years

### Step 2: Calculate the True Discount (TD)
The formula for True Discount is:
\[ \text{True Discount} = \frac{\text{Banker's Gain} \times 100}{r \times t} \]

Substituting the values:
\[ \text{True Discount} = \frac{144 \times 100}{24 \times 8} \]

### Step 3: Simplify the Calculation
Calculating the denominator:
\[ 24 \times 8 = 192 \]
Now substituting back:
\[ \text{True Discount} = \frac{14400}{192} \]

### Step 4: Perform the Division
Calculating the division:
\[ \text{True Discount} = 75 \]

### Step 5: Calculate Present Worth (PW)
The formula for Present Worth is:
\[ \text{Present Worth} = \frac{\text{True Discount}^2}{\text{Banker's Gain}} \]

Substituting the values:
\[ \text{Present Worth} = \frac{75^2}{144} \]

### Step 6: Calculate the Square of True Discount
Calculating \(75^2\):
\[ 75^2 = 5625 \]

### Step 7: Perform the Division for Present Worth
Now substituting back into the formula:
\[ \text{Present Worth} = \frac{5625}{144} \]

### Step 8: Perform the Final Division
Calculating the division:
\[ \text{Present Worth} \approx 39.06 \]

### Final Answer
The present worth of the bill is approximately ₹39.06.

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