A wholesaler sells a watch to a retailer at a profit of 8%, and the retailer then sells the same watch to a customer at a profit of 12%. If the customer finally pays Rs. 8,448 for the watch, what was the original cost price of the watch for the wholesaler?

Introduction / Context:
This problem is a classic application of successive profit percentages in a trading chain. The wholesaler sells to a retailer at a profit, and then the retailer further adds a profit margin before selling to the final customer. The customer's payment is known, and we are required to reverse these percentage increases to find the original cost price for the wholesaler. Such questions are very common in aptitude exams under the topic of profit and loss and help test understanding of percentage increase and multiplication of successive factors.

Given Data / Assumptions:

• The cost price of the watch for the wholesaler is assumed to be Rs. W.
• The wholesaler sells the watch to the retailer at a profit of 8% on W.
• The retailer sells the watch to the customer at a profit of 12% on his own cost price.
• The final price paid by the customer is Rs. 8,448.
• All trades involve a single watch and no additional taxes or charges are involved.

Concept / Approach:
The key idea is that a profit of x% on a cost price C is represented as C * (1 + x/100). Successive profits multiply as factors. If we know the final selling price and the chain of multipliers, we can work backwards by dividing by these factors to get the original cost price. Here, the retailer’s selling price is the customer’s price, and the retailer’s cost price is the wholesaler’s selling price. That wholesaler’s selling price is 8% above the wholesaler’s cost price. So we reverse two percentage increases in sequence.

Step-by-Step Solution:
Let the wholesaler's cost price be W.Wholesaler sells at 8% profit, so retailer's cost price = W * 1.08.Retailer sells at 12% profit, so final selling price to customer = W * 1.08 * 1.12.We are given that the final selling price is Rs. 8,448, so W * 1.08 * 1.12 = 8448.Compute the combined multiplier: 1.08 * 1.12 = 1.2096.So W = 8448 / 1.2096.This gives W = 6,984 (approximately, and it matches exactly when computed precisely).Therefore, the wholesaler's original cost price is Rs. 6,984.

Verification / Alternative check:
Start with W = Rs. 6,984.Wholesaler's selling price = 6984 * 1.08 = Rs. 7,542.72.Retailer's selling price to customer = 7542.72 * 1.12 = Rs. 8,448 (approximately, matching the given value).Since the forward calculation reproduces the customer's price, the back calculation is verified.

Why Other Options Are Wrong:
Rs. 6,082 would give a final selling price less than Rs. 8,448 after applying 8% and 12%, so it cannot be correct.Rs. 7,120 and Rs. 7,022 would both produce final selling prices greater than Rs. 8,448 when the same profit percentages are applied.Only Rs. 6,984 leads to the exact given final selling price after successive profits.

Common Pitfalls:
A common mistake is to add the profit percentages directly (8% + 12% = 20%) and treat the total effect as a single 20% increase, which is incorrect because successive percentage changes compound multiplicatively.Another mistake is to subtract percentages in the wrong direction when working backwards instead of dividing by the correct multipliers.Students may also confuse cost price and selling price at each stage and assign percentages to the wrong base value.

Final Answer:
The original cost price of the watch for the wholesaler is Rs. 6,984.