ICSE Class 10 Answered
Le x be the number of articles purchased. The amount paid for the x articles is Rs 900.
So the price of the article = 900/x.
The number good articles = x-5.
The selling price is more than the purchase price by Rs 3 implies he sells at Rs(900/x +3) per article.
Therefore the amount he gets by selling (x-5) articles in good condition = number of artilcles sold * selling price = (x-5)(900/x +3) but this is equal to Rs150 profit. Or Rs(900+150) in cash. So,
(x-5)((900/x+3 ) = 1050. Multiply by x an we get:
(x-5)(900+3x) = 1050x Or
3x^2+(900-15)x-4500 = 1050x Or
x^2 +885x-1050x+4500 = 0 Or
3x^2 - 165x - 4500 = 0. This is a quadratic equation in x. This could be solved either by factorising the left side and equating each factor to zero. Or by the quadratic formula for roots: If ax^2+bx+c = 0, then x = {-b +or- (b^2-4ac)^0.5}/(2a). So,
x = [165 +or- sqrt(165^2- - 4*3*4500)^(1/2)]/(2*3)
= (165 +or- 285)/6
= 75.
So the number of articles he brought = 75
Tally:
No of articles : 900/75 =12.
The damaged =5. Good articles = 75 - 5 =70.
Selling price = 12+3 =15.
The amount of by sale of 70 articles = 70*15 = 1050
Profit = 1050 - 900 = 150