A sells a watch to B and makes a loss of 12%. B dismakes a profit of 12`1/2`% by selling the watch to C. If A sells the watch to B at the cost of which C pruchased it, then the percentage of profit or loss is

Options

A. 1% Loss
B. 1% Profit
C. 2% Loss
D. 2% profit

Answer

To solve the problem step by step, we will first define the cost price (CP) of the watch for A, then calculate the selling price (SP) for A when he sells to B, and subsequently find the selling price for B when he sells to C. Finally, we will determine the profit or loss percentage when A sells the watch at the cost price of what C purchased it for.

### Step 1: Assume the Cost Price of A
Let the cost price (CP) of the watch for A be ₹100.

**Hint:** Start by assuming a simple value for CP to make calculations easier.

### Step 2: Calculate the Selling Price of A to B
A sells the watch to B at a loss of 12%.
- Loss = 12% of 100 = 12
- Selling Price (SP) of A to B = CP of A - Loss = 100 - 12 = ₹88.

**Hint:** Use the formula SP = CP - (Loss% × CP) to find the selling price after a loss.

### Step 3: Calculate the Selling Price of B to C
B sells the watch to C at a profit of 12.5%.
- Profit = 12.5% of 88 = (12.5/100) × 88 = ₹11.
- Selling Price (SP) of B to C = CP of B + Profit = 88 + 11 = ₹99.

**Hint:** Use the formula SP = CP + (Profit% × CP) to find the selling price after a profit.

### Step 4: Determine the Selling Price of A when selling at C's Cost Price
According to the problem, A sells the watch to B at the cost price at which C purchased it, which is ₹99.

**Hint:** Recognize that A's selling price to B is equal to C's purchase price.

### Step 5: Calculate the Profit or Loss for A
Now we need to find out if A incurs a profit or a loss when selling at ₹99.
- Loss = CP of A - Selling Price of A = 100 - 99 = ₹1.

### Step 6: Calculate the Percentage of Loss
Now, we calculate the percentage of loss:
- Percentage of Loss = (Loss / CP of A) × 100 = (1 / 100) × 100 = 1%.

**Hint:** Use the formula for percentage loss: (Loss / CP) × 100 to find the percentage.

### Conclusion
A incurs a loss of 1% when selling the watch to B at the cost at which C purchased it.

**Final Answer:** 1% loss.