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

x^{2} + 100x = 7500 cross multiplying

x^{2} + 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

x^{2} + 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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