Question

A person on tour has $₹4200$ for his expenses. If he extends his tour for $3$ days, he has to cut down daily expenses by $₹70$. Find the original duration of the tour.

Answer 1

Step:Find the original duration of the tour.

Given, Total money a person has$=₹4200$

Let $x$ days be the duration of the tour.

Expense in a day $=\frac{4200}{x}$

Duration of the extended tour $=3days$

Then, Expense in a day $=\frac{4200}{x+3}$

As per the question, we get

$\frac{4200}{x}-\frac{4200}{x+3}=70$

$4200\left(\frac{1}{x}-\frac{1}{x+3}\right)=70$

$\Rightarrow \left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{70}{4200}$

$\Rightarrow \left(\frac{1}{x}-\frac{1}{x+3}\right)=\frac{1}{60}$

$\Rightarrow \frac{x+3-x}{x\left(x+3\right)}=\frac{1}{60}$

$\Rightarrow \frac{3}{x^2+3x}=\frac{1}{60}$

$\Rightarrow x^2+3x=180$

$\Rightarrow x^2+3x-180=0$

$\Rightarrow x^2+15x–12x–180=0$

$\Rightarrow x(x+15)–12(x+15)=0$

$\Rightarrow (x+15)(x–12)=0$

$\Rightarrow x+15=0orx–12=0$

$\Rightarrow x=-15orx=12$

Since x cannot be a negative So, $x=12$

Hence, the original duration of the tour is $12$ days.