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, 

₹ `(10,800)/x` – ₹ `(10,800)/(x + 4)` = ₹ 90 

⇒ `(10800x + 43200 - 10800x)/(x(x + 4)) = 90` 

⇒ `(43200)/(x^2 + 4x) = 90` 

⇒ x² + 4x = 480 

⇒ x² + 4x – 480 = 0 

⇒ x² + 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.