The true discount on a bill 24 months, hence at 24% per annum, is X 144. What will be the banker's discount?

Options

A. 1) 213.12
B. 2) 415
C. 3) 515.12
D. 4) 616

Answer

To solve the problem, we need to find the banker's discount given the true discount on a bill. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- True Discount (TD) = Rs. 144
- Time (T) = 24 months = 2 years
- Rate (R) = 24% per annum

### Step 2: Use the Formula for Banker's Gain
The formula relating true discount (TD) and banker's gain (BG) is:
\[ TD = \frac{BG \times 100}{R \times T} \]
We need to rearrange this formula to find the banker's gain (BG):
\[ BG = \frac{TD \times R \times T}{100} \]

### Step 3: Substitute the Values into the Formula
Now, substitute the values into the formula:
\[ BG = \frac{144 \times 24 \times 2}{100} \]

### Step 4: Calculate the Banker's Gain
First, calculate the numerator:
\[ 144 \times 24 = 3456 \]
Then multiply by 2:
\[ 3456 \times 2 = 6912 \]
Now divide by 100:
\[ BG = \frac{6912}{100} = 69.12 \]

### Step 5: Calculate the Banker's Discount
The banker's discount (BD) is given by the formula:
\[ BD = TD + BG \]
Substituting the values we have:
\[ BD = 144 + 69.12 = 213.12 \]

### Final Answer
The banker's discount is approximately Rs. 213.12.

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