By selling a rickshaw for ₹9240, Banst loses 12% For how much should he sell it to gain 12%?

Options

A. `13760`
B. `12760`
C. Rs. 11760
D. `21760`

Answer

To solve the problem step by step, we need to find the cost price of the rickshaw first, and then calculate the selling price required to gain 12%.

### Step 1: Find the Cost Price (CP)

Given that Banst sells the rickshaw for ₹9240 at a loss of 12%, we can use the formula for selling price (SP) when there is a loss:

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

Substituting the known values:

\[ 9240 = CP \times \left(1 - \frac{12}{100}\right) \]

This simplifies to:

\[ 9240 = CP \times \left(1 - 0.12\right) \]
\[ 9240 = CP \times 0.88 \]

Now, to find the cost price (CP), we rearrange the equation:

\[ CP = \frac{9240}{0.88} \]

Calculating this gives:

\[ CP = 10500 \]

### Step 2: Calculate the Selling Price for a Gain of 12%

Now that we have the cost price, we can find the selling price (SP) required for a gain of 12%. We use the formula for selling price when there is a gain:

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

Substituting the values we have:

\[ SP = 10500 \times \left(1 + \frac{12}{100}\right) \]

This simplifies to:

\[ SP = 10500 \times \left(1 + 0.12\right) \]
\[ SP = 10500 \times 1.12 \]

Calculating this gives:

\[ SP = 11760 \]

### Final Answer:
To gain 12%, Banst should sell the rickshaw for **₹11760**.

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