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. 2 more than what he paid for it. He got a profit of Rs. 80 on the whole transaction. Find the number of articles he bought.

Answer 1

Let the total number of articles be $n$.

Let the value of one article be $a$.

Given that trader bought $n$ articles for $Rs900$.

So that $n\times a=900$ and $a=\frac{900}{n}$

Also given that five of them were damaged, he sold the remaining articles for Rs. $2$ extra and he also got a Rs. $80$ profit.

So that the equation would be $(n-5)\times (a+2)=900+80$

⇒ $na-5a+2n-10=980.$

⇒ $900-5\times \frac{900}{n}+2n=990$ [∴ na = 900 and a = 900/n]

⇒ $2n-\frac{4500}{n}=90$

⇒ $n-\frac{2250}{n}=45$

⇒ $n^2-2250=45n$

⇒ $n^2-45n-2250=0$

⇒ $n^2-75n+30n-2250=0$

⇒ $n(n-75)+30(n-75)=0$

⇒ $(n-75)(n+30)=0$

⇒ $n=75$ or $-30$

Since $n$ is the number of goods, it is always positive.

Hence, number of articles he bought was $75.$