Q. 33

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.

Answer :

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 – –





x2 – 5x = 750


x2 – 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


x2 – 5x – 750 = 0


x2 – 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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