Question

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

Answer 1

SOLUTION:-

Given:

•A person on tour has Rs.4200 for his expenses.

•He extends his tour for 3 days, he cut down his daily expenses by Rs.70.

To find:

The original duration of the tour.

Explanation:

•Assume R days be the original duration of the tour.

•Since, increased duration of the tour,

=) (R+3) days.

Now,

$Daily \: expenses = \frac{Total \: amount}{Number \: o f \: days}$

According to the question:

$= > \frac{4200}{R} - \frac{4200}{R + 3} = 70 \\ \\ = > \frac{4200(R + 3) - 4200(R)}{R(R + 3)} = 70 \\ \\ = > \frac{4200(R + 3 - R)}{R(R + 3)} = 70 \\ \\ = > \frac{3}{R(R + 3)} = \frac{70}{4200} \\ \\ = > \frac{3}{R(R + 3)} = \frac{1}{60} \\ [cross \: multiplication] \\ = > R(R + 3) = 180 \\ \\ = > {R}^{2} + 3R - 180 = 0 \\ \\ = > {R}^{2} + 15R - 12R- 180 = 0 \\ \\ = > R(R + 15) - 12(R + 15) = 0 \\ \\ = > (R + 15)(R - 12) = 0 \\ \\ = > R + 15 = 0 \: \: \: \: or \: \: \: \: R - 12 = 0 \\ \\ = > R = - 15 \: \: \: \: or \: \: \: \: R = 12$

Number of the days can't be negative.

So,

R= 12 days.

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