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A person on tour has ₹$5,400$ for his expenses. If he extends his tour by $5$ days, he has to cut down his daily expenses by ₹$180$. Find the original duration of the tour and daily expense.
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Sol. Let original duration of the tour be $x$ days.
$\therefore$ Daily expense is $\frac{5400}{x}$
According to the question,
$\frac{5400}{x} - \frac{5400}{x+5} = 180$ (I) (2 Marks)
$\Rightarrow x^2 + 5x - 150 = 0$ (II) (1 Mark)
$\Rightarrow (x + 15) (x - 10) = 0$ (III) (1 Mark)
$\Rightarrow x = -15, 10$
$\therefore x \neq -15$
$\therefore x = 10$ (IV) ($\frac{1}{2}$ Mark)
$\therefore$ Original duration of tour is $10$ days and daily expense is ₹$540$. (V) ($\frac{1}{2}$ Mark)
$\therefore$ Daily expense is $\frac{5400}{x}$
According to the question,
$\frac{5400}{x} - \frac{5400}{x+5} = 180$ (I) (2 Marks)
$\Rightarrow x^2 + 5x - 150 = 0$ (II) (1 Mark)
$\Rightarrow (x + 15) (x - 10) = 0$ (III) (1 Mark)
$\Rightarrow x = -15, 10$
$\therefore x \neq -15$
$\therefore x = 10$ (IV) ($\frac{1}{2}$ Mark)
$\therefore$ Original duration of tour is $10$ days and daily expense is ₹$540$. (V) ($\frac{1}{2}$ Mark)