Question

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

Answer 1

Let the original duration of the tour be x days. Then,
`(4200)/(x)-(4200)/((x+3))=70`
`implies" "4200xx[(1)/(x)-(1)/((x+3))]=70implies((x+3)-x)/(x(x+3))=(70)/(4200)`
`implies" "x(x+3)=180impliesx^(2)+3x-180=0`
`implies" "x^(2)+15x-12x-180=0impliesx(x+15)-12(x+15)=0`
`implies" "(x+15)(x-12)=0impliesx+15=0" or "x-12=0`
`implies" "x=-15" or "x=12`
`implies" "x=12" "[because" number of days cannot be negative"].`
`:." "` original duration of the tour is 12 days.