Question

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

Answer 1

Let the original duration be n days.

Daily expense = `"Total budget"/"Number of days"`

Original daily expense = `5400/n`.

New duration = n + 5.

New daily expense = `5400/(n + 5)`

Given: New expense = Original expense – 180.

`5400/n - 5400/(n + 5) = 180`

`30/n - 30/(n + 5) = 1`

`30[(n + 5 - n)/(n(n + 5))] = 1`

`150/(n^2 + 5n) = 1`

⇒ n² + 5n – 150 = 0

n² + 15n – 10n – 150 = 0

n(n + 15) – 10(n + 15) = 0

⇒ (n – 10)(n + 15) = 0

Since n cannot be negative, n = 10.

Daily expense = `5400/10` = 540.

Original duration was 10 days and daily expense was 540.