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 whole transaction. Find the numbers of articles he bought.

Answer 1

Profit divided by profit on each item equal to no of fine articles that's 40 and 5 damaged so total is 45

Answer 2

Answer:

75

Step-by-step explanation:

Sol:

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.