Subjects algebra

Wristwatch Loss F03D8B

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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.