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.

Answer 1

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