CA Foundation · Quantitative Aptitude · Linear Inequalities
A school hall in Indore is rented for ₹4,000 plus ₹50 per guest for a function. The organiser's total budget is at most ₹10,000. If x is the number of guests, which is the range of x?
The number of guests lies in 0 ≤ x ≤ 120. The cost 4000 + 50x must not exceed ₹10,000, giving 50x ≤ 6000 and x ≤ 120, while guests cannot be negative. Reversing the inequality would wrongly allow budget overruns.
- A0 ≤ x ≤ 120Correct
- B0 ≤ x ≤ 80
- C0 ≤ x ≤ 200
- Dx ≥ 120
Explanation
Cost is 4000 + 50x ≤ 10000, so 50x ≤ 6000 and x ≤ 120. Guests cannot be negative, so 0 ≤ x ≤ 120. The option x ≥ 120 reverses the inequality sign.
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