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.
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Let the original duration of the tour = x days.
Total amount = ₹5,400
Original daily expense = ₹(5400/x)
After extending by 5 days, new daily expense = ₹5400/(x + 5)
Setting up the equation:
$$\frac{5400}{x} - \frac{5400}{x+5} = 180$$
$$5400(x+5) - 5400x = 180 \cdot x(x+5)$$
$$5400 \times 5 = 180x(x+5)$$
$$27000 = 180x^2 + 900x$$
$$x^2 + 5x - 150 = 0$$
Factorising:
$$x^2 + 15x - 10x - 150 = 0$$
$$x(x + 15) - 10(x + 15) = 0$$
$$(x - 10)(x + 15) = 0$$
$$x = 10 \quad \text{or} \quad x = -15$$
Since duration cannot be negative, x = 10.
Original duration = 10 days
Original daily expense = 5400/10 = ₹540
Source: Chapter 4, Quadratic Equations (Application-based problems)
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Explanation
- Examiners award marks for: correct variable definition (½ mark), setting up the equation (1 mark), simplifying to standard quadratic form (1 mark), correct factorisation (1 mark), rejecting negative root (½ mark), and stating both answers (1 mark).
- Always reject the negative value with a reason ("duration cannot be negative") — this is a common scoring point students miss.
- Divide through by 180 early to get simpler numbers before factorising.