A trader bought a number of articles for Rs 1,200. Ten were damaged and he sold each of the remaining articles at Rs 2 more than what he paid for it, thus getting a profit of Rs 60 on the whole transaction. Taking the number of articles he bought as x, form an equation in x and solve it.
Number of articles bought by the trader = x
It is given that the trader bought the articles for Rs 1200.
So the cost of one article = Rs `1200/x`
Ten articles were damaged So the number of articles left = x - 10
The selling price of each of (x - 10) articles Rs `(x - 10) (1200/x + 2)`
Profit = Rs 60
`∴ (x - 10)(1200/x + 2) - 1200 = 60`
1200 + 2x - 12000/x - 20 - 1200 = 60
`2x - 12000/x - 80 = 0`
`2x^2 - 80x - 12000 = 0`
`x^2 - 40x - 6000 = 0`
`x^2 - 100x + 60x - 6000 = 0`
x(x - 100) + 60(x - 100) = 0
x = 100, -60
Number of articles cannot be negative. So, x = 100.