Question

A trader bought a number of articles for Rs.900, five were damaged and he sold each of the rest at Rs.2 more than what he paid for it. If on the whole he gains Rs.80, find the number of articles bought.

Answer 1

Let the number of articles purchase = x.
total cost of x articles =Rs 900
Hence cost of 1 article = $Rs\frac{900}{x}$.
Sale price per article $=\frac{900}{x}+2$
But he sold (x - 5) articles, since 5 are damaged.
Hence the total sales price = (x - 5)(\frac{900}{x + 2}) = (x - 5)$\frac{(900+2x)}{x}$
Profit = Sales price - cost price $=(x-5)\frac{(900+2x)}{x-900}$ = Rs 80 (given)
$\Rightarrow$ (x - 5)(900 + 2x) = x(980)
$900x-4500+2x^2-10x=980x$
$2x^2-90x-4500=0$
$x^2-45x-2250=0$
$x^2-75x+30x-2250=0$
$x(x-75)+30(x-75)=0$
$(x-75)(x+30)=0\to x=75$ (taking only positive root)
Hence, the number of articles bought are 75.