A wholesaler sells a watch to a retailer at a gain of 32%, and the retailer then sells it to a customer at a loss of 20%. If the customer pays Rs. 1953.60 for the watch, what was the cost price of the watch for the wholesaler?

Introduction / Context:
This profit and loss problem involves two levels of transactions: from wholesaler to retailer and from retailer to customer. The watch changes hands twice, with a gain in the first step and a loss in the second. You are given the final selling price to the customer and must work backwards through both percentage changes to find the original cost price for the wholesaler.

Given Data / Assumptions:
- The customer's purchase price (final selling price) = Rs. 1953.60. - Retailer sells at a loss of 20% relative to his cost price. - Wholesaler sells to retailer at a gain of 32% relative to the wholesaler's cost price. - There are no additional markups or discounts beyond these percentages. - We must find the original cost price of the watch for the wholesaler.

Concept / Approach:
Let the wholesaler's cost price be W. The retailer buys the watch at a 32% gain on W, so retailer's cost price R = 1.32 * W. The retailer then sells at a loss of 20%, so customer's price C = 0.80 * R. We know that C = Rs. 1953.60. Using the relation C = 0.80 * 1.32 * W, we can solve for W directly by dividing the customer price by the product 0.80 * 1.32.

Step-by-Step Solution:
Step 1: Let W be the wholesaler's cost price. Step 2: Wholesaler gains 32%, so retailer's cost price R = 1.32 * W. Step 3: Retailer sells at a loss of 20%, so customer's price C = 0.80 * R. Step 4: Substitute R: C = 0.80 * 1.32 * W. Step 5: Multiply the factors: 0.80 * 1.32 = 1.056. Step 6: So, C = 1.056 * W. Step 7: Given C = 1953.60, so 1.056 * W = 1953.60. Step 8: Therefore, W = 1953.60 / 1.056. Step 9: W = 1850 rupees.

Verification / Alternative check:
We can forward-check. If wholesaler's cost price is Rs. 1850, then wholesaler sells to retailer at a 32% gain: R = 1850 * 1.32 = Rs. 2442. The retailer then sells at a 20% loss: C = 2442 * 0.80 = Rs. 1953.60, which matches the given customer price. This verifies that the cost price for the wholesaler is indeed Rs. 1850.

Why Other Options Are Wrong:
If W were Rs. 2063, Rs. 2394, or Rs. 1637, computing forward with 32% gain and then 20% loss would not produce 1953.60. These are distractor values that may result if the percentages are applied in the wrong order or if profit and loss are calculated on the wrong base. Only Rs. 1850 leads exactly to the customer price of 1953.60 with the given gain and loss percentages.

Common Pitfalls:
Students may confuse which percentage applies to which stage, or they may attempt to combine 32% gain and 20% loss into a single percentage without considering that they are applied on different amounts. Another mistake is to treat the loss as 20% of the wholesaler's cost instead of the retailer's cost. The safest approach is to define variables clearly and move step by step from wholesaler to retailer to customer or in reverse when solving for the original cost price.

Final Answer:
The watch originally cost the wholesaler Rs. 1850.