A wholesaler sells a watch to a retailer at a profit of 20%, and the retailer then sells it to a customer at a loss of 10%. If the customer pays Rs 874.80 for the watch, what was the wholesaler's original cost price?

Introduction / Context:
This question tests your understanding of successive profit and loss in a trade chain, where a wholesaler sells to a retailer and the retailer sells to a customer. You need to correctly apply percentage profit and percentage loss in reverse to find the original cost price of the wholesaler, given the final selling price to the customer. This is a standard type of profit and loss question used in many aptitude exams.

Given Data / Assumptions:

• Let the wholesaler's cost price be Rs x.
• Wholesaler sells to retailer at a gain of 20%.
• Retailer sells to customer at a loss of 10%.
• Final selling price to the customer = Rs 874.80.
• We assume there are no other hidden costs such as tax, transport, or commission.

Concept / Approach:
The approach uses the relation between cost price and selling price with percentage changes:

• For profit p%, SP = CP * (1 + p / 100).
• For loss l%, SP = CP * (1 - l / 100).
• Here, the retailer's cost is the wholesaler's selling price.
• We work backward from the final selling price to find the wholesaler's cost price.

By expressing everything in terms of x, we can set up a simple equation and solve it.

Step-by-Step Solution:
Step 1: Let wholesaler cost price = x. Step 2: Wholesaler gains 20%, so retailer cost price = x * (1 + 20 / 100) = 1.2x. Step 3: Retailer sells at a loss of 10%. So final selling price = 1.2x * (1 - 10 / 100) = 1.2x * 0.9 = 1.08x. Step 4: Given final selling price = Rs 874.80. So 1.08x = 874.80. Step 5: Solve for x: x = 874.80 / 1.08 = 810. Step 6: Therefore, the wholesaler's cost price was Rs 810.

Verification / Alternative check:
We can verify by moving forward through the trade chain:

• Wholesaler cost price = Rs 810.
• Wholesaler sells at 20% profit: 20% of 810 = 0.2 * 810 = 162. So wholesaler selling price = 810 + 162 = Rs 972.
• Retailer cost price = Rs 972.
• Retailer sells at 10% loss: 10% of 972 = 97.20. So final selling price = 972 - 97.20 = Rs 874.80.

This matches the given customer payment exactly, so the calculation and the value of x are correct.

Why Other Options Are Wrong:
Rs 945: If this were the wholesaler cost, the final selling price would not match 874.80 after applying the given percentages.
Rs 994 and Rs 675: Similar checks with profit and loss formulas show that these starting values do not lead to a final price of Rs 874.80.
Thus, only Rs 810 produces the correct final customer price and satisfies all conditions.

Common Pitfalls:
A very common mistake is to add or subtract percentages directly instead of applying them multiplicatively. Another frequent error is to treat both 20% and 10% as profits or to ignore that the second transaction is a loss. Some students also incorrectly assume that the total percentage change is 20% minus 10% = 10% profit, which is not valid here because the percentages are taken on different bases. Always carefully track which price each percentage applies to.

Final Answer:
The wholesaler originally paid Rs 810 for the watch.