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.

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*x = 900 ; so x = 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(900/n) + 2n = 990 [as nx = 900 and x = 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 no. of goods, it is always positive

so the number of articles he bought was 75

Hope it helps....Thumbs up plz!!

Let no. of articles = x and cost of each one be Rs. y.

According to the question,

xy = 900. Therefore, y = 900 / x. ------------ (1)

And, (x-5) (y+2) = 900 + 80

Implies, xy + 2x - 5y - 10 = 900 + 80 (since xy = 900 so they are the same thing)

Implies, 2x - 5y - 90 = 0

Implies, 2x - 5(900 / x) - 90 = 0

Implies, 2x² - 4500 - 90x = 0

Implies, x² - 45x - 2250 = 0

Implies, x²- 75n + 30n - 2250 = 0

Implies, x(x- 75) +30(x - 75) = 0

Implies,(x - 75) (x + 30) = 0

Therefore, x = 75 and x = -30.

Since no. of articles can never be -ve, x = 75.

Therefore, Number of articles = 75.

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*x = 900 ; so x = 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(900/n) + 2n = 990 [as nx = 900 and x = 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 no. of goods, it is always positive

so the number of articles he bought was 75

Hope it helps....Thumbs up plz!!