A Watch Dealer Incurs an Expense of Rs. 150 for Producing Every Watch GMAT Problem Solving

Question: A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100. If he produces 1500 watches, what is the number of watches that he must sell during the season in order to breakeven, given that he is able to sell all the watches produced?

1. 500
2. 700
3. 800
4. 1000
5. 1100

Answer:

Approach Solution (1):

Let us assume the dealer sells “y” watches in season at Rs. 250 and hence there are (1500 – y) watches that are sold off the season at Rs. 100
Break even is when the Total Selling Price = S.P = Total Cost Price (C.P) and there is no profit/ loss
Total S.P = y * 250 + (1500 – y) * 100
Total C.P = (1500 * 150) + Fixed charges = (1500 * 150) + 30,000
According to the question: (y * 250) + (1500 – y) * 100 = 1500 * 150 + 30,000 (Break even)
150y = 1500 (50) + 30,000
1500 (50 + 20) = 1500 * 70
y = 1500 * \(\frac{70}{150}\)= 700

Correct Option: B

Approach Solution (2):

Total cost to produce 1500 watches = (1500 * 150 + 30,000) = Rs. 2,55,000
Let he sells x watches during the season, therefore number of watches sold after the season = (1500 – x)
Revenue earned on the sale of 1500 watches = 250 * x + (1500 – x) * 100 = 150x + 150000
Now, break-even is achieved if production cost is equal to the selling price
Therefore, 150x + 150000 = 2,55,000
x = 700

Correct Option: B

Approach Solution (3):

Let x = number of watches he sells during the season @250
Let y = number of watches he does not sell during the season and must sell for 100
All 1,500 watches produced get sold
x + y = 1,500 --- (eq. 1)
To break-even:
100y + 250x >/= 150 (1500) + 30,000
Reducing each side of the inequality by common factor of 50
2y + 5x >/= 3 (1500) + 600
Substitute equation 1: x + y = 1500
y = 1500 – x
2 (1500 – x) + 5x >/= 5100
3000 – 2x + 5x >/= 5100
3x >/= 2100
x >/= 200

He needs to sell 700 watches during the season to break-even

Correct Option: B

“A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100. If he produces 1500 watches, what is the number of watches that he must sell during the season in order to breakeven, given that he is able to sell all the watches produced?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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