A salesman earns a commission of `4%` on the value of sales he makes. If he sells a tv at `80%` of Marked price, then the commission earned by him is Rs.`114.4`. Find the M.P fo that tv? (in Rs.)

Options

A. A)2550
B. B)2575
C. C)5550
D. D)3575

Answer

To find the marked price (M.P.) of the TV, we can follow these steps:

### Step 1: Understand the relationship between commission and sales price
The salesman earns a commission of 4% on the value of sales he makes. If he sells the TV at 80% of the marked price (M.P.), we can express this mathematically.

### Step 2: Set up the equation
Let the marked price of the TV be \( M.P. \). The selling price (S.P.) of the TV is 80% of the marked price:
\[ S.P. = 0.80 \times M.P. \]

The commission earned by the salesman is 4% of the selling price:
\[ \text{Commission} = 4\% \text{ of } S.P. = \frac{4}{100} \times S.P. \]

### Step 3: Substitute the selling price into the commission formula
Substituting the expression for S.P. into the commission formula gives:
\[ \text{Commission} = \frac{4}{100} \times (0.80 \times M.P.) = \frac{4 \times 0.80}{100} \times M.P. \]
\[ \text{Commission} = \frac{3.2}{100} \times M.P. \]

### Step 4: Set the equation equal to the commission earned
According to the problem, the commission earned is Rs. 114.4. Therefore, we can set up the equation:
\[ \frac{3.2}{100} \times M.P. = 114.4. \]

### Step 5: Solve for the marked price
To find the marked price, we can rearrange the equation:
\[ M.P. = \frac{114.4 \times 100}{3.2}. \]

Calculating this gives:
\[ M.P. = \frac{11440}{3.2} = 3575. \]

### Conclusion
The marked price of the TV is Rs. 3575.

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