Question

A trader bought a number of articles for Rs 900. 5 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 Rs 900.

So that  n×a = 900 and a = 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)×(a + 2) = 900 + 80

⇒ na - 5a +2n -10 = 980.

⇒ 900 - 5(900/n) + 2n = 990   [∴ na = 900 and a = 900/n]

⇒ 2n - (4500/n) = 90

⇒ n - (2250/n) = 45

⇒ n2 - 2250 = 45n

⇒ n2 -45n -2250 = 0

⇒ n2 - 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

Answer 2

Answer:

let the total no of aarticles be n

let the value of one article ne a

given:

        na=900

       a=900/n

(n-5)*(a+2)=980

na-5a+2n=990

900-5(900/n)+2n=990

2n-4500/n=90

n2-2250=45n

n2-45-2250=0

n(n-75)30(n-75)

(n+30)  (n-75)

n=-30  n=75

sine the no of arrticles cannot be in negative

the answer is 75