A wholesale shopkeeper purchased 200 identical watches and sold the first 50 at 10% profit, the next 50 at 20% profit, the next 50 at 25% profit and the last 50 at 40% profit. If his total profit was Rs 19000, at what total cost did he buy the watches?

Correct option is B

Given:
Total number of watches = 200.
Selling details:
First 50 sold at 10% profit.
Next 50 sold at 20% profit.
Next 50 sold at 25% profit.
Last 50 sold at 40% profit.
Total profit = Rs 19,000.
Solution:
Step 1: Represent the cost price of one watch.
Let the cost price (C.P.) of one watch be Rs x.
Then, the total cost price of 200 watches = 200x.
Step 2: Calculate the selling price (S.P.) of each batch of 50 watches.
First 50 watches at 10% profit:
Selling price for 50 watches = 50 × x × 1.10 = 55x.
Next 50 watches at 20% profit:
Selling price for 50 watches = 50 × x × 1.20 = 60x.
Next 50 watches at 25% profit:
Selling price for 50 watches = 50 × x × 1.25 = 62.5x.
Last 50 watches at 40% profit:
Selling price for 50 watches = 50 × x × 1.40 = 70x.
Step 3: Total selling price of 200 watches.
Total selling price = 55x + 60x + 62.5x + 70x = 247.5x.
Step 4: Calculate the total profit.
Total profit = Total selling price - Total cost price.
Given that the total profit is Rs 19000:
247.5x - 200x = 19000.
47.5x = 19000.
x = 19000 / 47.5 = 400.
Step 5: Calculate the total cost price of the watches.
Total cost price = 200x = 200 × 400 = 80000.
Final Answer: (b) Rs 80000