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 watches during the season, he sells it for Rs.250. If he fails to do so, he has to sell the 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 break down even, given that he is able to sell all the watches produced?

Answer 1

Hint: According to the question, we need to know first whether he is doing a profit or loss in the starting. For that we need to calculate his cost price and selling price. After getting the profit or loss, then we will calculate the number of watches to even the breakdown. For that, the condition is that the cost price should be equal to the selling price.

Formula used: \[{\text{Profit = Selling}}\,{\text{Price}}\,{\text{ - }}\,{\text{Cost}}\,{\text{Price}}\]

Complete step-by-step solution:
From the question given, we can say that:
Expense incurred \[ = 150\]
The additional expenditure \[ = 30000\]
Production expense for producing 1 watch \[ = 150\]
Here, we will take the production cost here as the cost price.
So, production expense for producing 1500 watches \[ = 150 \times 1500 + 30000\]
Therefore, production expense for producing 1500 watches \[ = 255000\]
So, we got that the cost price for 1500 watches \[ = 255000\]
Now, we will take the amount for the sale of 1500 watches as the selling price.
The total amount received for the sale of 1500 watches \[ = 1200 \times 250 + 300 \times 100\]
Therefore, the total amount received for the sale of 1500 watches \[ = 330000\]
So, the selling price for 1500 watches \[ = 330000\]
Now, we can see that the cost price is less than the selling price. Thus, profit is earned.
\[{\text{Profit = Selling}}\,{\text{Price}}\,{\text{ - }}\,{\text{Cost}}\,{\text{Price}}\]
\[ \Rightarrow {\text{Profit = 330000 - 255000}}\]
\[ \Rightarrow {\text{Profit = 75000}}\]
Now, we will see for the breakdown even. For this condition, we know that the cost price should be equal to the selling price. So, let the number of watches sold be\[{\text{x}}\].
We know that the cost price \[ = 255000\]
New Selling price \[{\text{ = 250x + (1500 - x)100}}\]
We know that selling price should be equal to cost price. So:
\[ \Rightarrow {\text{255000 = 250x + (1500 - x)100}}\]
Now, we have to solve for \[{\text{x}}\], and we get:
\[ \Rightarrow {\text{x = 700}}\]

Therefore, we got that the number of watches that he should sell to even the breakdown is \[{\text{700}}\].

Note: In Mathematics, profit and loss is generally used to know the rate of a product in the market and to know whether the business is going on profit or loss. If the cost price of a product is less than the selling price, it is profit. If the cost price is more than the selling price of a product, it is a loss.