By selling a stool for Rs 72 a carpenter faces a loss of 10%. How much percentage would he gain or lose by selling the stool for rs 96

Options

A. profit 10%
B. loss 25%
C. loss 16%
D. profit 20%

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Determine the Cost Price (CP) of the Stool
Given that selling the stool for Rs. 72 results in a loss of 10%, we can express the selling price (SP) in terms of the cost price (CP).

Let the cost price of the stool be \( CP = 100x \).

Since there is a loss of 10%, the selling price can be calculated as:
\[ SP = CP - (10\% \text{ of } CP) = CP \times (1 - 0.10) = CP \times 0.90 \]
Thus, we have:
\[ SP = 100x \times 0.90 = 90x \]

### Step 2: Set Up the Equation
We know that the selling price when sold for Rs. 72 is:
\[ 90x = 72 \]

### Step 3: Solve for x
To find the value of \( x \), we rearrange the equation:
\[ x = \frac{72}{90} = \frac{8}{10} = 0.8 \]

### Step 4: Calculate the Cost Price
Now we can calculate the cost price (CP):
\[ CP = 100x = 100 \times 0.8 = 80 \]

### Step 5: Determine the Selling Price for Rs. 96
Next, we need to find out the profit or loss when the stool is sold for Rs. 96. The selling price now is:
\[ SP = 96 \]

### Step 6: Calculate the Profit
The profit can be calculated as:
\[ \text{Profit} = SP - CP = 96 - 80 = 16 \]

### Step 7: Calculate the Profit Percentage
Finally, we can calculate the profit percentage using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{16}{80} \right) \times 100 = 20\% \]

Thus, the carpenter would gain a profit of **20%** by selling the stool for Rs. 96.