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