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A person on a tour has ₹ $4,200$ for expenses. If he extends his tour for $3$ days, he has to cut down his daily expenses by ₹ $70$. Find the original duration of the tour.
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Let the original duration of the tour be $x$ days
Original daily expenses = ₹ $\frac{4200}{x}$
New daily expenses = ₹ $\frac{4200}{x+3}$
$\frac{4200}{x} - \frac{4200}{x+3} = 70$ (2 Marks)
$\Rightarrow x^2 + 3x - 180 = 0$ (1 1/2 Marks)
$\Rightarrow (x + 15)(x – 12) = 0$ (1 Mark)
$\Rightarrow x = -15, x = 12$
$x = -15$ (rejected)
$x = 12$ (1/2 Mark)
$\therefore$ Original duration of the tour = $12$ days
Original daily expenses = ₹ $\frac{4200}{x}$
New daily expenses = ₹ $\frac{4200}{x+3}$
$\frac{4200}{x} - \frac{4200}{x+3} = 70$ (2 Marks)
$\Rightarrow x^2 + 3x - 180 = 0$ (1 1/2 Marks)
$\Rightarrow (x + 15)(x – 12) = 0$ (1 Mark)
$\Rightarrow x = -15, x = 12$
$x = -15$ (rejected)
$x = 12$ (1/2 Mark)
$\therefore$ Original duration of the tour = $12$ days