Answer :

Let the original duration of the tour be x days

Original daily expenses =


If he extends his tour by 4 days his daily expenses =


According to the question – –



taking LCM



x2 + 4x = 480 cross multiplying


x2 + 4x – 480 = 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 = 4 c = – 480


= 1. – 480 = – 480


And either of their sum or difference = b


= 4


Thus the two terms are 24 and – 20


Difference = 24 – 20 = 4


Product = 24. – 20 = – 480


x2 + 24x – 20x – 480 = 0


x(x + 24) – 20(x + 24) = 0


(x + 24) (x – 20) = 0


(x + 24) = 0 or (x – 20) = 0


x = – 24, x = 20


x = 20 (number of days cannot be negative)


Hence the original price of tour is 20 days


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