Question

A person on tour has Rs.360 for his expenses.if he extends his tour for 4 days ,he has to cut down his daily expenses by Rs.3.find the original duration of the tour

Answer 1

Amount with the person = Rs 360 Let the original number of duration of the tour be x days Daily expenses per day = Rs 360/x Given that his tour is extended for 4 days Hence daily expenses per days = Rs 360/(x + 4) Therefore ⇒ 360x + 1440 – 360x = 3(x2 + 4x) ⇒ 1440 = 3x2 + 12x ⇒ 3x2 + 12x – 1440 = 0 ⇒ x2 + 4x – 480 = 0 ⇒ x2 + 24x – 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 Since x cannot be negative, x = 20 Hence his original duration of the tour is Rs 20