Question

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

Answer 1

Please see the attachment

Answer 2

Let the original duration of the tour be x days.

A/C,

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

$\longrightarrow$$\sf\red{4200((x + 3) - x) = 70 \times x \times (x + 3)}$

$\longrightarrow$$\sf\red{180 = x(x + 3)}$

$\longrightarrow$$\sf\red{{x}^{2} + 3x - 180 = 0}$

$\longrightarrow$$\sf\red{(x + 15)(x - 12) = 0}$

$\longrightarrow$$\sf\red{x = - 15 \: or \: x = 12}$

As the number of days cannot be negative, x ≠ -15 ,so x = 12

Hence, the original duration of the tour = 12 days