CA Foundation · Quantitative Aptitude · Linear Inequalities
A cab driver in Pune earns ₹18 per km on trips. His daily fuel and maintenance cost is ₹6 per km plus a fixed daily cost of ₹960. Which inequality gives the number of km (x) he must drive in a day to earn a daily profit of at least ₹1,200?
The correct inequality is 18x − 6x − 960 ≥ 1,200. Profit equals revenue minus variable cost minus fixed cost, and 'at least' means greater than or equal to the target. This simplifies to 12x ≥ 2,160, so he must drive at least 180 km.
- A18x − 6x − 960 ≥ 1,200Correct
- B18x − 6x + 960 ≥ 1,200
- C18x − 6x − 960 ≤ 1,200
- D18x − 960 ≥ 1,200
Explanation
Profit = revenue − variable cost − fixed cost = 18x − 6x − 960 = 12x − 960. 'At least ₹1,200' means profit ≥ 1,200, giving 12x − 960 ≥ 1,200, so x ≥ 180. Option B adds the fixed cost, and option D ignores the variable cost.
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