A person sells a watch at a profit of 26%. If he had bought it at 20% less and sold for ₹81.60 less, he would have gained 32%. What is the original costprice (in ₹) of the watch?

Options

A. 400
B. 480
C. 450
D. 360

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Define Variables
Let the original cost price of the watch be \( CP = x \).

### Step 2: Calculate Selling Price with 26% Profit
The selling price (SP) when sold at a profit of 26% can be calculated as:
\[ SP = CP + 26\% \text{ of } CP = x + 0.26x = 1.26x \]

### Step 3: Calculate New Cost Price
If the watch was bought at 20% less, the new cost price (New CP) would be:
\[ New \, CP = CP - 20\% \text{ of } CP = x - 0.20x = 0.80x \]

### Step 4: Calculate New Selling Price
If the watch is sold for ₹81.60 less than the original selling price, the new selling price (New SP) would be:
\[ New \, SP = SP - 81.60 = 1.26x - 81.60 \]

### Step 5: Set Up the Equation for 32% Profit
According to the problem, if the watch is sold at the new selling price, the profit would be 32%. Therefore, we can express this as:
\[ New \, SP = New \, CP + 32\% \text{ of } New \, CP \]
Substituting the values:
\[ 1.26x - 81.60 = 0.80x + 0.32 \times 0.80x \]
Calculating \( 0.32 \times 0.80x \):
\[ 0.32 \times 0.80x = 0.256x \]
Thus, we can rewrite the equation as:
\[ 1.26x - 81.60 = 0.80x + 0.256x \]
Combining like terms on the right side:
\[ 1.26x - 81.60 = 1.056x \]

### Step 6: Solve for x
Now, we can isolate \( x \):
\[ 1.26x - 1.056x = 81.60 \]
\[ 0.204x = 81.60 \]
Dividing both sides by 0.204:
\[ x = \frac{81.60}{0.204} = 400 \]

### Conclusion
The original cost price of the watch is \( \text{₹} 400 \).