A wholesaler sells a watch to a retailer at a gain of 37%, and the retailer sells it to a customer at a loss of 25%. If the customer pays Rs 2620.125, what was the original cost price of the watch for the wholesaler?

Introduction / Context:
This question extends the idea of successive percentage changes in a trade chain where first a wholesaler gains, and then a retailer incurs a loss. Despite opposite directions, both percentage changes are multiplicative. The final price given is the sale price to the customer, and we must work backwards to find what the wholesaler originally paid for the watch.

Given Data / Assumptions:

• The wholesaler sells to the retailer at a gain of 37%.
• The retailer sells to the customer at a loss of 25% on his purchase price.
• The customer pays Rs 2620.125 for the watch.
• We assume there are no additional discounts, taxes or costs.

Concept / Approach:
Let the wholesaler cost price be CPw. When he sells to the retailer at 37% gain, the retailer buying price is CPw * 1.37. The retailer then sells at a loss of 25%, so selling price to the customer is (CPw * 1.37) * 0.75. This combined multiplier is 1.37 * 0.75 = 1.0275. Given the final price, we can divide by 1.0275 to find CPw.

Step-by-Step Solution:
Let CPw be the cost price of the watch for the wholesaler.Price to retailer = CPw * (1 + 37 / 100) = CPw * 1.37.Retailer sells at 25% loss, so selling price to customer SP = (CPw * 1.37) * (1 - 25 / 100) = CPw * 1.37 * 0.75.Thus SP = CPw * 1.0275.Given SP = Rs 2620.125.So CPw * 1.0275 = 2620.125.CPw = 2620.125 / 1.0275 = Rs 2550.

Verification / Alternative check:
Starting with CPw = Rs 2550, price to retailer at 37% gain is 2550 * 1.37 = Rs 3493.5. Retailer then sells at 25% loss: SP = 3493.5 * 0.75 = Rs 2620.125, which exactly matches the given customer price. This confirms that the wholesaler cost price of Rs 2550 is correct.

Why Other Options Are Wrong:
Numbers like Rs 2692, Rs 3327 or Rs 2408, when multiplied by 1.0275, do not yield Rs 2620.125. They would produce higher or lower final prices, so they do not satisfy the given chain of profit and loss. Only Rs 2550 reproduces the exact selling price to the customer after both percentage changes.

Common Pitfalls:
Some candidates incorrectly subtract or add percentages directly instead of using multiplicative factors, or they may confuse the base for loss (retailer cost price) with the base for gain (wholesaler cost). Another frequent mistake is rounding off early, which can disturb the final answer when decimals are involved. Keeping all steps algebraic until the end helps maintain accuracy.

Final Answer:
The original cost price of the watch for the wholesaler was Rs 2550.