Q. 374.5( 8 Votes )

A dealer sells an article for Rs. 75 and gains as much per cent as the cost price of the article. Find the cost price of the article.

Answer :

Let the cost price of the article be x

Gain percent x%

According to the given condition,


(cost price + gain = selling price)


taking LCM

by cross multiplying

x2 + 100x = 7500  


x2 + 100x – 7500 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 100 c = – 7500


= 1. – 7500 = – 7500


And either of their sum or difference = b


= 100


Thus the two terms are 150 and – 50


Difference = 150 – 50 = 100


Product = 150. – 50 = – 7500


x2 + 150x – 50x – 7500 = 0


x(x + 150) – 50(x + 150) = 0


(x + 150) (x – 50) = 0


(x + 150) = 0 or (x – 50) = 0


x = 50 (x ≠ - 150 as price cannot be negative)


Hence the cost price of the article is Rs 50

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