Amount with the person =Rs360 Let the original number of duration of the tour be x days Daily expenses per day =Rs
360
x
Given that his tour is extended for 4 days Hence daily expenses per days =Rs
360
x+4
Therefore
360
x
−
360
x+4
=3 ⇒
360(x+4)−360x
x(x+4)
=3
⇒360x+1440−360x=3(x2+4x)
⇒1440=3x2+12x ⇒3x2+12x−1440=0 ⇒x2+4x−480=0 ⇒x2+24x−20x−480=0 ⇒x(x+24)−20(x+24)=0 ⇒(x+24)(x−20)=0 ⇒(x+24)=0 or (x−20)=0 ∴x=−24 or x=20 since x cannot be negative, x=20 Hence his original duration of the tour is 20 days.