By selling a bike for Rs. 38000, a person loses 20%. For how much should he sell the bike to gain 15%?

Options

A. Rs. 68120
B. Rs. 54625
C. Rs. 47500
D. Rs. 55625

Answer

To solve the problem step by step, we need to determine the cost price (CP) of the bike first, and then calculate the selling price (SP) required to achieve a 15% gain.

### Step 1: Find the Cost Price (CP) of the bike
Given that selling the bike for Rs. 38,000 results in a loss of 20%, we can use the formula for loss:

\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} \]

Since the loss is 20% of the cost price, we can express this as:

\[ \text{Loss} = 20\% \text{ of CP} = \frac{20}{100} \times \text{CP} = 0.2 \times \text{CP} \]

So, we can rewrite the equation as:

\[ 38000 = \text{CP} - 0.2 \times \text{CP} \]

This simplifies to:

\[ 38000 = 0.8 \times \text{CP} \]

Now, we can solve for CP:

\[ \text{CP} = \frac{38000}{0.8} = 47500 \]

### Step 2: Calculate the Selling Price (SP) for a 15% Gain
Now that we have the cost price, we can find the selling price for a 15% gain. The formula for gain is:

\[ \text{Selling Price} = \text{Cost Price} + \text{Gain} \]

Where the gain is 15% of the cost price:

\[ \text{Gain} = 15\% \text{ of CP} = \frac{15}{100} \times \text{CP} = 0.15 \times \text{CP} \]

Substituting the value of CP we found:

\[ \text{Gain} = 0.15 \times 47500 = 7125 \]

Now, substituting back into the selling price formula:

\[ \text{SP} = \text{CP} + \text{Gain} = 47500 + 7125 = 54625 \]

### Final Answer:
The selling price to gain 15% should be Rs. 54,625.

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