The cost price of a shirt is increased by 20%. A trader who revised the selling price of the shirt to maintain the same profit percentage. Noted that he got Rs 10 more in profit on selling one shirt after he revised the selling price. What is his new profit (in Rs)?

Options

A. 50
B. 100
C. 60
D. 40

Answer

To solve the problem step by step, let's denote the following:

- Let the original cost price (CP) of the shirt be \( C \).
- Let the original selling price (SP) of the shirt be \( S \).
- Let the original profit be \( P \).

### Step 1: Determine the original profit
The profit is calculated as:
\[ P = S - C \]

### Step 2: Calculate the new cost price after a 20% increase
The cost price is increased by 20%. Therefore, the new cost price (CP') is:
\[ CP' = C + 0.2C = 1.2C \]

### Step 3: Maintain the same profit percentage
To maintain the same profit percentage, the selling price must also be adjusted. The new selling price (SP') is calculated based on the original selling price increased by the same percentage:
\[ SP' = S + 0.2S = 1.2S \]

### Step 4: Calculate the new profit
The new profit (P') can be calculated as:
\[ P' = SP' - CP' \]
Substituting the values we have:
\[ P' = 1.2S - 1.2C \]
Factoring out 1.2, we get:
\[ P' = 1.2(S - C) = 1.2P \]

### Step 5: Relate the new profit to the original profit
According to the problem, the new profit is Rs 10 more than the original profit:
\[ P' = P + 10 \]
Substituting \( P' \) from the previous step:
\[ 1.2P = P + 10 \]

### Step 6: Solve for the original profit (P)
Rearranging the equation:
\[ 1.2P - P = 10 \]
This simplifies to:
\[ 0.2P = 10 \]
Now, solving for \( P \):
\[ P = \frac{10}{0.2} = 50 \]

### Step 7: Calculate the new profit
Now that we have the original profit \( P \), we can find the new profit:
\[ P' = 1.2P = 1.2 \times 50 = 60 \]

### Final Answer
The new profit is Rs 60.

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