Question

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

Answer 1

Let the original duration of tour be x days.

Amount with the person is ₹ 4200.

Daily expenses = ₹ `4200/x`

Given, tour extended for 3 days.

Hence, total number of days = (x + 3) days

∴ Daily expenses = ₹ `4200/((x + 3))`

According to the question.

`4200/x - 4200/(x + 3) = 70`

⇒ `4200(1/x - 1/(x + 3)) = 70`

⇒ `60[(x + 3 - x)/(x(x + 3))] = 1`

⇒ 180 = x² + 3x

⇒ x² + 3x – 180 = 0

⇒ x² + 15x – 12x – 180 = 0

⇒ x(x + 15) – 12(x + 15) = 0

⇒ (x + 15)(x – 12) = 0

∴ x + 15 = 0 and x – 12 = 0

or x = –15 and x = 12

Since, x cannot be negative.

So, x = 12

Thus, the original duration of the tour is 12 days.