When an article is sold for Rs 388, there is a loss of 3%. What is the selling price (in Rs) of the article, if it is sold at a gain of 8%?

Options

A. 412
B. 444
C. 432
D. 460

Answer

To solve the problem, we need to find the cost price of the article first and then calculate the selling price when it is sold at a gain of 8%.

### Step 1: Find the Cost Price (CP)
We know that when the article is sold for Rs 388, there is a loss of 3%. This means that the selling price (SP) is 97% of the cost price (CP).

Using the formula:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]

We can rearrange this to find the cost price:
\[ CP = \frac{SP}{1 - \frac{Loss\%}{100}} \]

Substituting the values:
\[ CP = \frac{388}{1 - \frac{3}{100}} \]
\[ CP = \frac{388}{0.97} \]
\[ CP = 400 \]

### Step 2: Calculate the Selling Price at a Gain of 8%
Now that we have the cost price, we can find the selling price when there is a gain of 8%.

Using the formula:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]

Substituting the values:
\[ SP = 400 \times \left(1 + \frac{8}{100}\right) \]
\[ SP = 400 \times 1.08 \]
\[ SP = 432 \]

### Final Answer:
The selling price of the article, if it is sold at a gain of 8%, is Rs 432.

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