A shopkeeper marked a computer table for Rs. 7,200. He allows a discount of 10% on it and yet makes a profit of 8%. What will be his gain percentage if he does NOT allow any discount?

Options

A. 0.18
B. 0.02
C. 0.09
D. 0.2

Answer

To solve the problem step by step, we need to find the cost price (CP) of the computer table first, and then calculate the gain percentage if no discount is allowed.

### Step 1: Calculate the Selling Price (SP) after Discount
The marked price (MP) of the computer table is Rs. 7,200. The shopkeeper allows a discount of 10%.

\[ \text{Discount} = \text{MP} \times \frac{\text{Discount Percentage}}{100} = 7200 \times \frac{10}{100} = 720 \]

Now, we can find the selling price (SP) after the discount:

\[ \text{SP} = \text{MP} - \text{Discount} = 7200 - 720 = 6480 \]

### Step 2: Calculate the Cost Price (CP)
We know that the selling price (SP) is Rs. 6,480 and the profit percentage is 8%. We can use the formula for profit to find the cost price (CP):

\[ \text{SP} = \text{CP} + \text{Profit} \]

Where profit can be expressed as:

\[ \text{Profit} = \text{CP} \times \frac{\text{Profit Percentage}}{100} = \text{CP} \times \frac{8}{100} \]

Thus, we can rewrite the equation:

\[ 6480 = \text{CP} + \left(\text{CP} \times \frac{8}{100}\right) \]

This simplifies to:

\[ 6480 = \text{CP} \left(1 + \frac{8}{100}\right) = \text{CP} \times \frac{108}{100} \]

Now, solving for CP:

\[ \text{CP} = \frac{6480 \times 100}{108} = \frac{648000}{108} = 6000 \]

### Step 3: Calculate Gain Percentage if No Discount is Allowed
If no discount is allowed, the selling price (SP) will be equal to the marked price (MP), which is Rs. 7,200.

Now, we can calculate the gain percentage using the formula:

\[ \text{Gain Percentage} = \left(\frac{\text{SP} - \text{CP}}{\text{CP}}\right) \times 100 \]

Substituting the values:

\[ \text{Gain Percentage} = \left(\frac{7200 - 6000}{6000}\right) \times 100 = \left(\frac{1200}{6000}\right) \times 100 = 20\% \]

### Final Answer
The gain percentage if the shopkeeper does not allow any discount is **20%**.

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