Question

A trader bought a number of articles for Rs. 900 five articles were found damaged. He sold each of remaining articles at Rs. 2 more than he paid for it. He got a profit of Rs. 80 on the whole transaction. Find the number of articles he bought .

Answer 1

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.

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

Step-by-step explanation: