Question

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

Answer 1

Let the original duration of the tour be $x$ days. Then, the increased duration of the tour is $(x+3)$ days.

Daily expenses when the tour is of x days = $\frac{4200}{x}$

Daily expenses when the tour is of $(x+3)$ days = $\frac{4200}{x+3}$

According to the question,

$\frac{4200}{x}-\frac{4200}{x+3}=70$

$\frac{4200(x+3)-4200x}{x(x+3)}=70$

$\frac{60\times 3}{x^2+3x}=1$

$180=x^2+3x$

$x^2+3x-180=0$

$(x+15)(x-12)=0$

$x=12$

Therefore, original duration of tour $=12$ days.