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 [tex]=\frac{12000}{x}[/tex]
Given that number of day is increased by 2 more days, that is number of days is x+2.
New daily expense per day [tex]\frac{12000}{x+2}[/tex]
Given that this new daily expenses are 300 less than original.
That is [tex]\frac{12000}{x}-\frac{12000}{x+2}=300[/tex]
[tex]\frac{12000(x+2)-12000x}{x(x+2)}=300[/tex]
[tex]\frac{24000}{x(x+2)}=300[/tex]
[tex]x(x+2)=\frac{24000}{300}[/tex]
[tex]x^{2}+2x-80=0[/tex]
(x-8)(x+10)=0
x=8 or -10.
Since number of days cannot be negative, duration of the tour planned=8.
