On selling an article for Rs 170,a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees :
एक वस्तु को 170 में बेचने पर, एक दुकानदार को 15% की हानि होती है। तदनुसार, उसे 20% लाभ पाने के लिए उस वस्तु को कितने रुपयों में बेचना चाहिए?

Options

A. A)212.5
B. B)240
C. C)210
D. D)215.5

Explanation

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the given selling price (SP) and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)
The shopkeeper sells the article for Rs 170 and incurs a loss of 15%.

Loss percentage = 15%

This means that the selling price (SP) is 85% of the cost price (CP). We can express this relationship mathematically:

\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]

Substituting the values we have:

\[ 170 = CP \times \left(1 - \frac{15}{100}\right) \]

\[ 170 = CP \times 0.85 \]

To find CP, we rearrange the equation:

\[ CP = \frac{170}{0.85} \]

Calculating this gives:

\[ CP = 200 \]

### Step 2: Determine the Selling Price for a 20% Profit
Now that we have the cost price, we need to find the selling price (SP2) that would give a profit of 20%.

Profit percentage = 20%

This means that the selling price (SP2) is 120% of the cost price (CP). We can express this relationship as:

\[ SP2 = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]

Substituting the values we have:

\[ SP2 = 200 \times \left(1 + \frac{20}{100}\right) \]

\[ SP2 = 200 \times 1.20 \]

Calculating this gives:

\[ SP2 = 240 \]

### Conclusion
To gain a profit of 20%, the shopkeeper must sell the article for Rs 240.

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