Question

A person on tour has Rs.10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by Rs.90. Find the original duration of the tour.

Answer 1

Let the original duration of tour be x days
Amount with the person is Rs 10800
Daily expenses = Rs$\frac{10800}{x}$
Given tour extended for 4 more days
Hence total number of days = (x + 4) days
Daily expenses = $\frac{10800}{x+4}$ Rs [10800/(x + 4)]
By the given problem, we have
$\frac{10800}{x}$ -$\frac{10800}{x+4}$ =90

$10800(\frac{1}{x}-\frac{1}{x+4}=90$

$\frac{120(x+4-x)}{\left(x\right)(x+4)}=1$

$480=x^2+4x$

$x^2+4x-480=0$

$x^2+(24-20)x-480=0$

$x^2+24x-20x-480=0$

$x(x+24)-20(x+24)=0$
$(x+24)(x–20)=0$
Hence x = -24 as x cannot be negative
Thus the original duration of tour is 20 days.