Question

a person on tour has rs 4200 for his expenses. if he extends his tour for 3days, he has to cut down his daily expenses by rs 70 the original duration of tour is x days then x square = ​

Answer 1

Correct question:-

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

Supposition:-

• let the duration of the tour be X days
• expenses for 1 day = $\bf\bigg(\dfrac{4200}{x}\bigg)Rs.$

If the tour is extended for 3 days, the expenses per day will be:- $\bf\bigg(\dfrac{4200}{x+3}\bigg)Rs.$

According to the question:-

:$\implies$$\bf\bigg(\dfrac{4200}{x}\bigg)-70 =\bigg(\dfrac{4200}{x+3}\bigg)$

:$\implies$$\bf\bigg(\dfrac{4200}{x}\bigg)-\bigg(\dfrac{4200}{x+3}\bigg) = 70$

:$\implies$$\bf\dfrac{4200(x+3)-4200x}{x (x+3)} = 70$

:$\implies$$\bf 4200x+12600-4200x= 70x²+210x$

:$\implies$$\bf 70x²+210x-12600$

:$\implies$$\bf x²+3x-180 = 0$

:$\implies$$\bf x²+(15-12)x-180 = 0$

:$\implies$$\bf x²+15x-12x-180 = 0$

:$\implies$$\bf x(x+15)-12(x+15) = 0$

:$\implies$$\bf x = -15, 12$

since, duration can never be -ve hence, 12 days is right answer