If a man were to sell his hand cart for Rs. 720, he would lose 25%. At what price must he sell it to gain 25%?

Options

A. Rs.1200
B. Rs.960
C. Rs.1152
D. Rs.768

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the hand cart based on the selling price (SP) when there is a loss of 25%. Then, we will calculate the selling price required to achieve a gain of 25%.

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

Given that selling the hand cart for Rs. 720 results in a loss of 25%, we can set up the following relationship:

Let the cost price (CP) be \( x \).

Since a loss of 25% means the selling price is 75% of the cost price, we can write:

\[ SP = CP - (25\% \text{ of } CP) = 75\% \text{ of } CP \]

This can be expressed mathematically as:

\[ 720 = 0.75x \]

### Step 2: Solve for CP

To find \( x \), we rearrange the equation:

\[ x = \frac{720}{0.75} \]

Calculating this gives:

\[ x = 720 \div 0.75 = 720 \times \frac{100}{75} = 720 \times \frac{4}{3} = 960 \]

So, the cost price (CP) of the hand cart is Rs. 960.

### Step 3: Calculate the Selling Price for a Gain of 25%

Now, to find the selling price (SP) for a gain of 25%, we use the formula:

\[ SP = CP + (25\% \text{ of } CP) = 125\% \text{ of } CP \]

This can be expressed mathematically as:

\[ SP = 1.25 \times CP \]

Substituting the value of CP:

\[ SP = 1.25 \times 960 \]

Calculating this gives:

\[ SP = 1200 \]

### Final Answer

Thus, the selling price at which he must sell the hand cart to gain 25% is Rs. 1200.

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