a person on tour has Rs4200 for his expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs70. find the original duration of the tour.
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Then the person extends the tour for 3 days = (x+3) days.
Given that he has to cut down his daily expenses by Rs 70.
4200/x - 4200/x+3 = 70
On cross-multiplication, we get
4200(x + 3) - 4200x/x(x+3) = 70
4200x + 12600 - 4200x/70x(x+3)
12600 = 70(x^2 + 3x)
12600 = 70x^2 + 210x
-70x^2 -210x + 12600 = 0
-70(x^2 + 3x - 180) = 0
x^2 + 3x - 180 = 0
x^2 -12x + 15x - 180 = 0
x(x-12) + 15(x -12) = 0
x = 12 (or) x = -15.
The value of x cannot be -ve.So, x = 12.
Therefore the original duration of the tour = 12 days.
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