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

Given

Total money a person has = Rs 4200

Let the duration of tour = x days

Expense in a day = 4200/x

Duration of extended tour = 3 days

Then,

Expense in a day = 4200/(x + 3)

(4200/x) = {4200/(x + 3)} + 70

(4200/x) = (4200 + 70x + 210)/(x + 3)

On calculating further, we get,

4200x + 12600 = 4200x + 70x2 + 210x

70x2 + 210x – 12600 = 0

x2 + 3x – 180 = 0

x2 + 15x – 12x – 180 = 0

x(x + 15) – 12(x + 15) = 0

(x + 15) (x – 12) = 0

x = -15 and x = 12

Since x cannot be a negative

Therefore, x = 12

Hence, the original duration of tour is 12 days
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