Question

A person on tour has rs. 360 for his daily expenses. if he exceeds his tour program me by four days, he must cut down his daily expenses by rs 3 per day. find the number of days of his tour program me.

Answer 1

Amount with the person = Rs 360
Let the original number of duration of the tour be x days
Daily expenses per day = Rs 360/x
Given that his tour is extended for 4 days
Hence daily expenses per days = Rs 360/(x + 4)
= 360(x+4) - 360x / x(x+4) = 3

= 360x + 1440 – 360x = 3(x^2 + 4x)
=  1440 = 3x^2 + 12x
=  3x^2 + 12x – 1440 = 0
=  x^2 + 4x – 480 = 0
=  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 or x = 20
Since x cannot be negative, x = 20
Hence his original duration of the tour is Rs 20

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Answer 2

Answer:

The original duration of the tour is 20 days.

Solution:

Let us assume that the original duration for the tour is x.

So the daily expense for the person is

If he extends his tour 4 days then total days of tour is (x+4) days.

Then the daily expense for the person is

So as per the solution,

x=-24 or x=20  

So as x cannot be negative, so x=20

So the total duration of the tour is 20 days.