Wristwatch Loss F03D8B
1. **State the problem:** A wristwatch is sold at an 18% loss. If sold for 69 more, there would be a 5% gain. Find the cost price (CP) of the wristwatch. Also, find the total loss if 150 watches are sold at the loss price.
2. **Define variables:** Let the cost price be $x$.
3. **Write equations for selling prices:**
- Selling price at 18% loss: $$SP_1 = x - 0.18x = 0.82x$$
- Selling price at 5% gain: $$SP_2 = x + 0.05x = 1.05x$$
4. **Use the given difference in selling prices:**
$$SP_2 - SP_1 = 69$$
Substitute:
$$1.05x - 0.82x = 69$$
$$0.23x = 69$$
5. **Solve for $x$:**
$$x = \frac{69}{0.23} = 300$$
6. **Interpretation:** The cost price of the wristwatch is 300.
7. **Calculate loss per watch:**
Loss = Cost price - Selling price at loss
$$= 300 - 0.82 \times 300 = 300 - 246 = 54$$
8. **Calculate total loss for 150 watches:**
$$150 \times 54 = 8100$$
**Final answers:**
- Cost price of the wristwatch is 300.
- Total loss on selling 150 watches is 8100.