Question

A trader bought a number of articles for
1,200. Ten were damaged and he sold each
of the remaining articles at 2 more than what
he paid for it, thus getting a profit of
60 on the whole transaction ?
Taking x as the number of articles he bought, form an equation in x and solve it​

Answer 1

Given :

As the C.P of x articles is Rs.1200,

∴ CP. of one article = Rs 1200/x

As the selling price of each article is Rs 2 more than its C.P,

∴ S.P of each article = Rs 1200/x + 2

Since 10 articles were damaged, therefore, the number of articles left for selling = x - 10.

S.P. of all articles (worth selling) =Rs(x - 10) (1200/x + 2).

As the trader earns a net profit of Rs.60,

∴ (x - 10) (1200/x+2) = 1200 +60

= (x -10). (1200 + 2x)/x = 1260

= (x -10) (1200+ 2x) = 1260x

= 1200x + 2x² - 12000 - 20x - 1260x = 0

= 2x² - 80x - 12000 = 0

= x² - 40x - 6000 = 0

= x² -100x + 60x - 6000 = 0

= x(x-100) + 60(x- 100) = 0

= (x - 100) (x + 60) = 0

∴ x = 100 or x = -60 but x cannot be negative,

∴ x = 100