If the price of a book is reduced by Rs. 5, a person can buy 4 more books for Rs. 600. Find the original price of the book.

Let the original price of the book be Rs x

Number of books bought at original price for 600 =

If the price of a book is reduced by Rs. 5, then new price of book is Rs (x – 5)

Number of books bought at reduced price =

According to the question – –

x^{2} – 5x = 750

x^{2} – 5x – 750 = 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 = – 5 c = – 750

= 1. – 750 = – 750

And either of their sum or difference = b

= – 5

Thus the two terms are – 30 and 25

Difference = – 30 + 25 = – 5

Product = – 30.25 = – 750

x^{2} – 5x – 750 = 0

x^{2} – 30x + 25x – 750 = 0

x(x – 30) + 25(x – 30) = 0

(x + 25) (x – 30) = 0

(x + 25) = 0 or (x – 30) = 0

x = – 25 , x = 30

x = 30 (Price cannot be negative)

Hence the original price of the book is Rs 30.

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