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

Answer:

Duration of the tour he planned first is 8 days.

Step-by-step explanation:

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

Let x be the number of days.

Then daily expenses per day $=\frac{12000}{x}$

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

New daily expense per day $\frac{12000}{x+2}$

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

That is $\frac{12000}{x}-\frac{12000}{x+2}=300$

              $\frac{12000(x+2)-12000x}{x(x+2)}=300$

                  $\frac{24000}{x(x+2)}=300$

                  $x(x+2)=\frac{24000}{300}$

                    $x^{2}+2x-80=0$

                    (x-8)(x+10)=0

                     x=8 or -10.

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