John lent Rs. 2,550 to Mohan at `7*5` per cent per annum. If Mohan discharges the debt after 8 months by giving an old black and white television and Rs. `1,422*50`. Find the price of the television.

Answer

To find the price of the television that Mohan gave to John, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 2,550
- Rate of interest (R) = 7.5% per annum
- Time (T) = 8 months = \( \frac{8}{12} \) years = \( \frac{2}{3} \) years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{2550 \times 7.5 \times \frac{2}{3}}{100} \]
Calculating the interest:
\[ SI = \frac{2550 \times 7.5 \times 0.6667}{100} = \frac{2550 \times 5}{100} = \frac{12750}{100} = 127.50 \]

### Step 3: Calculate the Total Amount (A)
The total amount that Mohan needs to pay back is the sum of the principal and the interest:
\[ A = P + SI \]
Substituting the values:
\[ A = 2550 + 127.50 = 2677.50 \]

### Step 4: Set up the equation for the cost of the television
According to the problem, Mohan discharges his debt by giving an old black and white television and Rs. 1,422.50. Therefore, we can write:
\[ \text{Cost of TV} + 1422.50 = 2677.50 \]

### Step 5: Solve for the cost of the television
Rearranging the equation to find the cost of the television:
\[ \text{Cost of TV} = 2677.50 - 1422.50 \]
Calculating the cost:
\[ \text{Cost of TV} = 1255 \]

### Final Answer
The price of the television is **Rs. 1,255**.

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