A person on tour has Rs 360 for his expense. If he extends his tour for 6 days, he has to cut down his daily expenses by Rs 3.Find the original duration of the tour.
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Answer:
Let the original duration of the tour be x days.
Total expenditure on tour =Rs.360
Expenditure per day =Rs.
x
360
Duration of the extended tour =(x+4) days
Expenditure per day according to new schedule =Rs.
x+4
360
It is given that the daily expenses are cut down by Rs. 3
∴
x
360
−
x+4
360
=3
⇒
x(x+4)
360(x+4)−360x
=3⇒
x(x+4)
360x+1440−360x
=3
⇒
x
2
+4x
1440
=3⇒x
2
+4x=480⇒x
2
+4x−480=0
⇒x
2
+24x−20x−480=0
⇒x(x+24)−20(x+24)⇒(x−20)(x+24)=0
⇒x−20=0orx+24=0⇒x=20,x=−24
But the number of days cannot be negative. So, x=20
Hence, the original duration of the tour was 20 days.
Answered By
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