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 multiplyingx^{2} + 100x = 7500

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 (x ≠ - 150 as price cannot be negative)

Hence the cost price of the article is Rs 50

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