Question

A trader bought a number of articles for Rs. 900. Five articles were found damaged. He sold each of the remaining articles at Rs. 80 in the whole transaction. Find the number of articles he bought.

Answer 1

Let the total no. of articles be n
Let the initial value of 1 article be x
The question says that he bought n articles for Rs. 900
so $n\times x=900$ so $x=\frac{900}{n}$
It also says that since five of them were damaged, he sold the remaining for Rs. 2 extra and he also got a Rs. 80 profit.
So the equation formed would be (n - 5) (x + 2) = 900 + 80
nx - 5x + 2n - 10 = 980
$900-5\left(\frac{900}{n}\right)+2n=990$ [as nx = 900 and $x=\frac{900}{n}$]
$2n-\left(\frac{4500}{n}\right)=90n-\left(\frac{2250}{n}\right)=45n^2-2250=45n{n}^2-45n-2250=0n^2-75n+30n-2250=0n(n-75)+30(n-75)=0(n-75)(n+30)=0n=75or-30$
Since n is the no. of goods, it is always positive.
So the number of articles he bought was 75