A wholesaler sells a watch to a retailer at a profit of 25%, and the retailer then sells it to a customer at a loss of 12%. If the customer pays Rs 1045 for the watch, what was the wholesaler's original cost price?

Introduction / Context:
This problem involves two successive transactions of the same product. The wholesaler first sells to the retailer at a profit, and the retailer then sells to the final customer at a loss. You are given the final selling price and must work backwards to find the wholesaler's original cost price. Understanding how sequential profit and loss percentages combine is crucial for such questions.

Given Data / Assumptions:

• Let wholesaler cost price be Rs x.
• Wholesaler profit = 25%; his selling price to retailer = 1.25x.
• Retailer incurs a loss of 12% on his purchase price.
• Final selling price to customer = Rs 1045.
• No other costs or taxes are involved.

Concept / Approach:
Since the retailer's cost price is the wholesaler's selling price, we proceed as follows:

• Retailer cost price = 1.25x.
• Loss of 12% means final SP = 0.88 * retailer cost price.
• So final SP = 0.88 * 1.25x.
• Set this equal to Rs 1045 and solve for x.

The multiplication of 1.25 and 0.88 gives the combined effect on the wholesaler's cost price.

Step-by-Step Solution:
Step 1: Let wholesaler CP = x. Step 2: Wholesaler sells at a profit of 25%, so his SP = 1.25x. Step 3: Retailer buys at 1.25x and sells at a loss of 12%. Step 4: Retailer SP to customer = 1.25x * (1 - 12 / 100) = 1.25x * 0.88. Step 5: Compute the product: 1.25 * 0.88 = 1.10. Step 6: So final SP = 1.10x = Rs 1045. Step 7: Solve for x: x = 1045 / 1.10 = 950. Step 8: Therefore, the wholesaler's original cost price was Rs 950.

Verification / Alternative check:
Work forward from CP = Rs 950:

• Wholesaler sells at 25% profit: 25% of 950 = 0.25 * 950 = Rs 237.50.
• Wholesaler SP = 950 + 237.50 = Rs 1187.50.
• Retailer cost price = Rs 1187.50.
• Retailer sells at 12% loss: 12% of 1187.50 = 0.12 * 1187.50 = Rs 142.50.
• Final SP = 1187.50 - 142.50 = Rs 1045.

The final price matches the given amount paid by the customer, confirming that the wholesaler cost price is correct.

Why Other Options Are Wrong:
Rs 1149, Rs 1244, and Rs 751 all fail when you apply the sequence of 25% profit followed by 12% loss. None of them yields a final selling price of exactly Rs 1045. Only Rs 950, when processed through both steps, gives the correct final value, so it is the unique correct answer.

Common Pitfalls:
Some learners mistakenly add or subtract percentages (for example, 25% profit and 12% loss gives net 13% profit), which is incorrect because they are applied on different bases. Others might try to treat Rs 1045 as being 12% below a certain value without accounting for the earlier 25% profit. Always relate each percentage to the correct cost or selling price at that stage of the transaction chain.

Final Answer:
The wholesaler originally purchased the watch for Rs 950.