The cost price of a table is ₹ 3,200. A merchant wants to make 25 % profit by selling it. At the the time of sale he de clares a discount of 20 % on the marked price. The marked price (in ₹) is(

Options

A. 5000
B. 6000
C. 4000
D. 4500

Answer

To find the marked price (MP) of the table, we can follow these steps:

### Step 1: Determine the desired selling price (SP) for a 25% profit.
The cost price (CP) of the table is ₹3,200. To find the selling price that includes a 25% profit, we can use the formula:

\[ SP = CP + (Profit \% \times CP) \]

Calculating the profit:

\[ Profit = 25\% \text{ of } 3200 = \frac{25}{100} \times 3200 = 800 \]

Now, we can find the selling price:

\[ SP = 3200 + 800 = 4000 \]

### Step 2: Understand the relationship between marked price (MP), selling price (SP), and discount.
The merchant declares a discount of 20% on the marked price. The relationship can be expressed as:

\[ SP = MP - (Discount \% \times MP) \]

This can also be written as:

\[ SP = MP \times (1 - \frac{Discount \%}{100}) \]

### Step 3: Substitute the known values into the equation.
We know the selling price (SP) is ₹4,000 and the discount is 20%. Therefore, we can substitute these values into the equation:

\[ 4000 = MP \times (1 - \frac{20}{100}) \]

This simplifies to:

\[ 4000 = MP \times (1 - 0.2) = MP \times 0.8 \]

### Step 4: Solve for the marked price (MP).
To find MP, we rearrange the equation:

\[ MP = \frac{4000}{0.8} \]

Calculating this gives:

\[ MP = 4000 \div 0.8 = 5000 \]

### Final Answer:
The marked price (MP) of the table is ₹5,000.

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