Mohan sold his watch at 10% loss. If he had sold it for 45 more, he would have made 5% profit. The selling price (in Rs) of the watch was

Options

A. 300
B. 900
C. 110
D. 270

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Problem
Mohan sold his watch at a 10% loss. If he had sold it for Rs. 45 more, he would have made a 5% profit. We need to find the selling price of the watch.

### Step 2: Let the Cost Price (CP) be 100
For simplicity, let's assume the cost price (CP) of the watch is Rs. 100.

### Step 3: Calculate the Selling Price at 10% Loss
If Mohan sold the watch at a 10% loss, the selling price (SP1) can be calculated as:
\[ SP1 = CP - (10\% \text{ of } CP) \]
\[ SP1 = 100 - (10\% \text{ of } 100) \]
\[ SP1 = 100 - 10 = 90 \]
So, the selling price at a 10% loss is Rs. 90.

### Step 4: Calculate the Selling Price at 5% Profit
If Mohan had sold the watch for Rs. 45 more, he would have made a 5% profit. The selling price (SP2) at 5% profit can be calculated as:
\[ SP2 = CP + (5\% \text{ of } CP) \]
\[ SP2 = 100 + (5\% \text{ of } 100) \]
\[ SP2 = 100 + 5 = 105 \]
So, the selling price at a 5% profit is Rs. 105.

### Step 5: Set Up the Equation
According to the problem, if he sold it for Rs. 45 more than the selling price at a 10% loss, it would equal the selling price at a 5% profit:
\[ SP1 + 45 = SP2 \]
Substituting the values we found:
\[ 90 + 45 = 105 \]
This confirms that our calculations are correct.

### Step 6: Find the Selling Price
From our calculations, we found that the selling price at a 10% loss is Rs. 90. Therefore, the selling price of the watch was:
\[ \text{Selling Price} = SP1 = 90 \text{ Rs.} \]

### Final Answer
The selling price of the watch was Rs. 90.

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