Question

A wholesaler bought 120 watches for Rs.30 each. He sold 50% of the watches for Rs.20 each, one – third at Rs.40 each and the rest for Rs.60. What was the wholesaler’s approximate profit per watch?
(a) Rs.3.3
(b) Rs.5
(c) Rs.7
(d) Rs.9
(e) Rs.11

Answer 1

Hint: Find the cost price for 120 watches which is the product of the number of watches and their cost. Now find the selling price of these 120 watches. To find the profit take the difference of SP and CP. Approximate profit per watch is profit by 120 watches.

Complete step-by-step answer:
The total number of watches bought by the wholesaler = 120
Cost of each watch = Rs. 30.
\[\therefore \] Total cost price of the watch = Total number \[\times \] cost of each watch
\[\therefore \] Total cost price of the watch = 120 \[\times \] 60 = Rs. 3600
\[\therefore \] Total cost price of the watch = Rs. 3600.
50% of total number of watches = 50% of 120
50% of total number of watches = \[\dfrac{50}{100}\times 120=\dfrac{120}{2}=60\].
Thus he sold 60 watches for Rs. 20 each.
\[\therefore \] Selling price of 60 watches = 60 \[\times \] 20 = Rs. 1200 – (1)
He sold \[{{\dfrac{1}{3}}^{rd}}\] of the watches at Rs. 40 each.
\[{{\dfrac{1}{3}}^{rd}}\] of the total number of watches = \[\dfrac{1}{3}\times 120=40\]
Thus he sold 40 watches for Rs. 40 each.
Remaining number of watches = total number of watches – 60 watches – 40 watches.
Remaining number of watches = 120 – 60 – 40 = 20 watches.
\[\therefore \] He sold 20 watches for Rs. 60 each.
\[\therefore \] Selling price 20 watches = 20 \[\times \] 60 = Rs. 1200 – (3)
Now add (1), (2) and (3) to get the total selling price.
\[\therefore \] Total selling price = 1200 + 1600 + 1200 = Rs. 4000.
To find the profit is the difference of selling price and cost price.
\[\therefore \] Profit = Selling price – Cost price = 4000 – 3600 = Rs. 400.
Hence the man earned a profit of Rs. 400 for the 120 watches.
The profit for one watch = \[\dfrac{Rs.400}{120}=Rs.3.3\]
Thus we found the wholesale’s approximate average profit as Rs. 3.3.
\[\therefore \] Option (a) is the correct answer.

Note: After finding the profit don’t forget to find the profit for individual watches. The formula for profit is profit. But if SP < CP, then it is a loss. Loss = CP – SP. So, compare the rate of SP and CP for finding profit / loss.