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

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by Naol

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by Naol

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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