A person on tour has Rs. 10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by Rs. 90. Find the original duration of the tour.

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

x^{2} + 4x = 480 cross multiplying

x^{2} + 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

x^{2} + 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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