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Question
The total cost price of a certain number of identical articles is Rs. 4800. By selling the articles at Rs. 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
Solution
Total cost of some articles = Rs. 4800
Let number of articles = x
S.P. of one article = Rs. 100
S.P. of x articles = Rs. 100x
Profit = Cost price of 15 articles
= `(15 xx 4800)/x = (72000)/x`
∴ S.P. = C.P. + Profit
⇒ 100x = 4800 + `(72000)/x`
⇒ 100x2 = 4800x + 72000
⇒ x2 = 48x + 720 ...(Dividing by 100)
⇒ x2 – 48x – 720 = 0
⇒ x2 – 60x + 12x – 720 = 0
⇒ x(x – 60) + 12(x – 60) = 0
⇒ (x – 60)(x + 12) = 0
Either x – 60 = 0, then x = 60
or x + 12 = 0, then x = –12 which is not possible.
∴ x = 60
Thus, required number of articles = 60
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