Let the original duration of the tour = x days.
Daily expenses = ₹ 4200/x
If tour is extended by 3 days, new duration = (x + 3) days
New daily expenses = ₹ 4200/(x + 3)
Setting up the equation:
According to the condition, daily expenses are cut by ₹ 70:
$$\frac{4200}{x} - \frac{4200}{x+3} = 70$$
$$4200(x+3) - 4200x = 70 \cdot x(x+3)$$
$$4200x + 12600 - 4200x = 70x^2 + 210x$$
$$12600 = 70x^2 + 210x$$
$$x^2 + 3x - 180 = 0$$
Factorising:
$$x^2 + 15x - 12x - 180 = 0$$
$$x(x + 15) - 12(x + 15) = 0$$
$$(x - 12)(x + 15) = 0$$
$$x = 12 \quad \text{or} \quad x = -15$$
Since duration cannot be negative, x = 12.
∴ The original duration of the tour is 12 days.
Source: Chapter 4, Quadratic Equations
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