Mike sold a watch at 5% loss. Had he sold it for $ 104 more, he would have gained 8%. Find the selling price of the watch.

Answer

To solve the problem step by step, let's denote the cost price (CP) of the watch as \( x \).

### Step 1: Calculate the Selling Price at 5% Loss
When Mike sells the watch at a 5% loss, the selling price (SP1) can be calculated as:
\[ SP1 = CP - (5\% \text{ of } CP) = x - 0.05x = 0.95x \]

### Step 2: Calculate the Selling Price for 8% Gain
If Mike had sold the watch for $104 more, he would have gained 8%. The selling price (SP2) in this case would be:
\[ SP2 = CP + (8\% \text{ of } CP) = x + 0.08x = 1.08x \]

### Step 3: Set Up the Equation
According to the problem, the difference between the two selling prices is $104:
\[ SP2 - SP1 = 104 \]
Substituting the values from Step 1 and Step 2:
\[ 1.08x - 0.95x = 104 \]

### Step 4: Simplify the Equation
Now, simplify the left side:
\[ (1.08 - 0.95)x = 104 \]
\[ 0.13x = 104 \]

### Step 5: Solve for Cost Price (CP)
Now, solve for \( x \):
\[ x = \frac{104}{0.13} = 800 \]

### Step 6: Calculate the Selling Price at 5% Loss
Now that we have the cost price, we can find the selling price at 5% loss:
\[ SP1 = 0.95x = 0.95 \times 800 = 760 \]

### Conclusion
Thus, the selling price of the watch is:
\[ \text{Selling Price} = 760 \]

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