Question

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

Answer 1

Let the original duration of the tour be x days. 

∴ Original daily expenses = ₹ `(10,800)/x` 

If he extends his tour by 4 days, then his new daily expenses =₹`(10,800)/(x+4)` 

According to the given condition, 

`Rs10800/x-Rs(10,800)/(x+4)=Rs90` 

⇒`(10800x+43200-10800x)/(x(x+4))=90` 

⇒`43200/(x^2+4x)=90` 

⇒`x^2+4x=480` 

⇒`x^2+4x-480=0` 

⇒`x^2+24x-20x-480=0` 

⇒`x(x+24)-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` 

∴` x=20`                                (Number of days cannot be negative)
Hence, the original duration of the tour is 20 days.