A shopkeeper incurs a loss of 8%, while selling an article for Rs. 46. What will be the selling price of the article to gain 6%?

Options

A. Rs.56
B. Rs.65
C. Rs.85
D. Rs.53

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first, and then calculate the selling price (SP) required to achieve a 6% profit.

### Step 1: Determine the Cost Price (CP)
Given that the shopkeeper incurs a loss of 8% when selling the article for Rs. 46, we can express this mathematically.

Loss of 8% means that the selling price (SP) is 92% of the cost price (CP).

So, we can set up the equation:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the values we have:
\[ 46 = CP \times \left(1 - \frac{8}{100}\right) \]
\[ 46 = CP \times 0.92 \]

To find CP, we rearrange the equation:
\[ CP = \frac{46}{0.92} \]
Calculating this gives:
\[ CP = 50 \]

### Step 2: Calculate the Selling Price for a 6% Profit
Now that we have the cost price, we can calculate the selling price needed to achieve a 6% profit.

A profit of 6% means that the selling price (SP) is 106% of the cost price (CP).

We can express this as:
\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
Substituting the values we have:
\[ SP = 50 \times \left(1 + \frac{6}{100}\right) \]
\[ SP = 50 \times 1.06 \]
Calculating this gives:
\[ SP = 53 \]

### Conclusion
The selling price of the article to gain a 6% profit is Rs. 53.

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