A trader buys a number of …

I think your question is "A trader buys a number of goods for rupees 900 and 5 goods are found to be faulty. he sells the remaining goods at Rs 2 per piece more than what he paid for it . He got a profit of 80 rupees in the whole transaction. find the number of good he bought"

Ans. Let Number of Article Bought = x

Total Amount Paid =  900         .................. (1)

Amount Paid for one article = \( 900 \over x\)

Faulty Article = 5
Remaining Article that He Sold = (x - 5)

Price for One article = \({900 \over x } + 2 = {900 +2x \over x}\)

Total Amount he Gain For all Article = \({900 +2x \over x} \times (x-5) = {(900x +2x^2 -4500 -10x)\over x} \)       ....... (2)

Profit = Total amount gain - total amount paid

So, from (2) and (1), We get 

=> Profit = \({(900x +2x^2 -4500 -10x)\over x} - {900} = {(900x +2x^2 -4500 -10x-900x )\over x} \)

=> \({2x^2 -4500 -10x \over x} \)       ...... (3)

Given Profit  =  80      ..... (4)

So from (3) and (4)

=> \({2x^2 -4500 -10x \over x} = 80 =>{2x^2 -4500 -10x = 80x } \)

=> \({2x^2 -4500 -10x - 80x } => {2x^2 -90x -4500 } \)

Divide it by 2, we get 

=> \({x^2 -45x -2250 } \)

=> x² - 75x + 30x - 2250 = 0 

=> x(x-75) +30(x-75) =0 

=> (x-75) (x+30) = 0

=> x = 75, -30  => \(\)

x cant not be -30,

So Number of Article Bought = 75