If you sell a watch for ₹100 Rupee the loss is double if you sell it for ₹160 Rupee. What is the purchase price of the watch?

Let the purchase price of the watch be \( x \) Rupees.

### Case 1: Selling the watch for ₹100
- Loss when selling for ₹100 = \( x - 100 \)

### Case 2: Selling the watch for ₹160
- Loss when selling for ₹160 = \( x - 160 \)

According to the problem, the loss in Case 1 is double the loss in Case 2. Hence, we can write the equation:
\[
x - 100 = 2(x - 160)
\]

### Solving the equation:
\[
x - 100 = 2x - 320
\]
\[
x - 2x = -320 + 100
\]
\[
-x = -220
\]
\[
x = 220
\]

Thus, the purchase price of the watch is ₹220.

Would you like further explanation on this, or do you have any questions?

Here are 5 related questions:
1. How do you calculate profit or loss in a transaction?
2. If the loss was triple, what would the selling price be?
3. How would the problem change if the loss was instead described in percentage terms?
4. What would happen if the watch was sold for ₹250? Would there be a profit or a loss?
5. How can we calculate the break-even price for a product?

**Tip:** Always verify the relationship between costs and selling prices by plugging them into different equations to avoid errors in word problems.

Learn how to solve a real-world profit and loss problem where selling a watch for ₹100 results in double the loss compared to selling it for ₹160. This step-by-step solution covers key algebraic concepts such as solving linear equations. Suitable for students in Grades 8-10.

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