The diff. between simple interest and true discount on Rs 2400 due 4 year hence at 5% per annum simple interest is.

Options

A. a)Rs 50
B. b)Rs 80
C. c)Rs 75
D. d)Rs 82

Answer

To solve the problem of finding the difference between simple interest and true discount on Rs 2400 due in 4 years at a rate of 5% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 2400 \) (Principal)
- \( R = 5 \) (Rate of interest)
- \( T = 4 \) (Time in years)

Substituting the values into the formula:
\[ SI = \frac{2400 \times 5 \times 4}{100} \]

### Step 2: Simplify the Calculation
Calculating the above expression:
\[ SI = \frac{2400 \times 20}{100} = \frac{48000}{100} = 480 \]
So, the Simple Interest is Rs 480.

### Step 3: Calculate True Discount (TD)
The formula for True Discount is given by:
\[ TD = \frac{P \times R \times T}{100 + R \times T} \]
Where:
- \( P = 2400 \)
- \( R = 5 \)
- \( T = 4 \)

Substituting the values into the formula:
\[ TD = \frac{2400 \times 5 \times 4}{100 + (5 \times 4)} \]

### Step 4: Simplify the Calculation for True Discount
Calculating the denominator:
\[ 100 + (5 \times 4) = 100 + 20 = 120 \]
Now substituting back into the True Discount formula:
\[ TD = \frac{2400 \times 20}{120} \]

### Step 5: Final Calculation for True Discount
Calculating the above expression:
\[ TD = \frac{48000}{120} = 400 \]
So, the True Discount is Rs 400.

### Step 6: Find the Difference Between SI and TD
Now, we need to find the difference:
\[ \text{Difference} = SI - TD = 480 - 400 \]

### Step 7: Final Result
Calculating the difference:
\[ \text{Difference} = 80 \]
Thus, the difference between Simple Interest and True Discount is Rs 80.