Question

a person on a tour has rupees 12000 for his daily expenses. In order to extend his journey for 2 more days he had to cut down his daily expenses by Rs.300 .find the duration of the tour he planned first.

Answer 1

Duration of the tour he planned first is 8 days.

Explanation:

Given that a person has 12000 rupees for his daily expenses.

Let x be the number of days.

Then daily expenses per day
`=(12000)/(x)`

Given that number of day is increased by 2 more days, that is number of days is x+2.

New daily expense per day
`(12000)/(x+2)`

Given that this new daily expenses are 300 less than original.

That is
`(12000)/(x)-(12000)/(x+2)=300`

`(12000(x+2)-12000x)/(x(x+2))=300`

`(24000)/(x(x+2))=300`

`x(x+2)=(24000)/(300)`

`x^(2)+2x-80=0`

(x-8)(x+10)=0

x=8 or -10.

Since number of days cannot be negative, duration of the tour planned=8.