Manish sold a watch at 5% loss. Had he sold it for Rs.312 more, he would have gained 8%.Find the selling price of the watch.

Answer

To find the selling price of the watch that Manish sold at a 5% loss, we can follow these steps:

### Step 1: Define the Variables
Let the cost price (CP) of the watch be Rs. X.

### Step 2: Calculate Selling Price at 5% Loss
When Manish sells the watch at a 5% loss, the selling price (SP) can be calculated as:
\[ SP_{5\% \text{ loss}} = CP - (5\% \text{ of } CP) = CP \times \left(1 - \frac{5}{100}\right) = X \times \frac{95}{100} = \frac{95X}{100} \]

### Step 3: Calculate Selling Price at 8% Gain
If Manish had sold the watch for Rs. 312 more, he would have gained 8%. The selling price at an 8% gain is:
\[ SP_{8\% \text{ gain}} = CP + (8\% \text{ of } CP) = CP \times \left(1 + \frac{8}{100}\right) = X \times \frac{108}{100} = \frac{108X}{100} \]

### Step 4: Set Up the Equation
According to the problem, if he had sold it for Rs. 312 more than the selling price at a 5% loss, it would equal the selling price at an 8% gain:
\[ SP_{5\% \text{ loss}} + 312 = SP_{8\% \text{ gain}} \]
Substituting the values we calculated:
\[ \frac{95X}{100} + 312 = \frac{108X}{100} \]

### Step 5: Solve for X
Now, we will solve for X:
1. Rearranging the equation:
\[ \frac{108X}{100} - \frac{95X}{100} = 312 \]
2. Combine the fractions:
\[ \frac{(108 - 95)X}{100} = 312 \]
\[ \frac{13X}{100} = 312 \]
3. Multiply both sides by 100:
\[ 13X = 31200 \]
4. Divide by 13:
\[ X = \frac{31200}{13} = 2400 \]

### Step 6: Calculate Selling Price at 5% Loss
Now that we have the cost price (CP) as Rs. 2400, we can find the selling price at 5% loss:
\[ SP_{5\% \text{ loss}} = \frac{95 \times 2400}{100} = 2280 \]

### Final Answer
The selling price of the watch is Rs. 2280.

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