The number of articles purchased = x
Total cost of buying x number of articles = Rs.1200 (given)
Purchase price = (Total cost)/(Number of articles) = 1200/x
Number of articles spoiled = 10 (Given)
Therefore: Number of articles sold = x - 10
Selling price = Purchase price + 2 (Given)
= 1200/x + 2
Profit made = Rs.60 (Given)
Total receipts from sale = (Cost of buying) +Profit = 1200 + 60 = 1260. ...
We can represent total receipts from sales also as:
(Number of articles sold)*(selling price) = (x - 10)*(1200/x + 2)
= 1200 - 12000/x + 2x - 20 = 2x + 1180 - 12000/x
Therefore:
1260 = 2x + 1180 - 12000/x
Taking all the terms of this equation on left hand side of equation and multiplying each term by -x/2 we get:
x^2 - 40x - 6000 = 0
This equation can be represented also as:
(x- 100)*(x + 60) = 0
Therefore x = 100 or - 60
As number of articles purchased cannot be negative, the number of articles purchase is 100.
Unit purchase price = 1200/x = 1200/100 = Rs.12
Unit sale price = (Unit purchase price) + 2 = 12 + 2 = Rs.14
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