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.

Let the cost price of the article be x

Gain percent x%


According to the given condition,


(cost price + gain = selling price)


taking LCM


x2 + 100x = 7500 cross multiplying


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 (price cannot be negative)


Hence the cost price of the article is Rs 50


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