By selling an article for ₹270, a shopkeeper gains 20% profit. If he sells it for ₹210, what is his gain or loss percentage ?

Options

A. Loss, `6 (2)/(3) %`
B. Gain , `7 (1)/(7) %`
C. Gain , `6 (2)/(3)%`
D. Loss, `7 (1)/(7)%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) of the article is ₹270 and the profit percentage is 20%, we can find the cost price using the formula:

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

Since profit is 20% of the cost price, we can express it as:

\[ \text{Profit} = \frac{20}{100} \times \text{CP} = \frac{1}{5} \times \text{CP} \]

Thus, we can rewrite the selling price equation as:

\[ \text{SP} = \text{CP} + \frac{1}{5} \times \text{CP} = \frac{6}{5} \times \text{CP} \]

Now substituting the selling price:

\[ 270 = \frac{6}{5} \times \text{CP} \]

### Step 2: Solve for CP
To find CP, we rearrange the equation:

\[ \text{CP} = 270 \times \frac{5}{6} \]

Calculating this gives:

\[ \text{CP} = 270 \times \frac{5}{6} = 225 \]

### Step 3: Calculate Loss or Gain when Selling at ₹210
Now, if the article is sold for ₹210, we need to determine if there is a gain or a loss. We compare the selling price (SP) with the cost price (CP):

\[ \text{SP} = 210, \quad \text{CP} = 225 \]

Since the selling price is less than the cost price, there is a loss.

### Step 4: Calculate the Loss Amount
The loss amount can be calculated as:

\[ \text{Loss} = \text{CP} - \text{SP} = 225 - 210 = 15 \]

### Step 5: Calculate Loss Percentage
The loss percentage is calculated using the formula:

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

Substituting the values we have:

\[ \text{Loss Percentage} = \left(\frac{15}{225}\right) \times 100 \]

Calculating this gives:

\[ \text{Loss Percentage} = \left(\frac{1}{15}\right) \times 100 = 6.67\% \]

This can be expressed as:

\[ 6 \frac{2}{3} \% \]

### Final Answer
The shopkeeper incurs a loss of \(6 \frac{2}{3} \%\).

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