CA Foundation · Quantitative Aptitude · Linear Inequalities
A firm's monthly cost is C = 15,000 + 20x and its revenue is R = 50x, where x is the number of units. For the firm to earn a profit of at least ₹ 30,000, the minimum number of units to be sold is:
The minimum is 1,500 units. Profit equals 30x − 15,000, and requiring at least ₹30,000 gives x ≥ 1,500. At exactly 1,500 units profit is ₹30,000, so the non-strict condition is met.
- A1,500Correct
- B1,000
- C1,501
- D1,200
Explanation
Profit = 50x − 15,000 − 20x = 30x − 15,000. Require 30x − 15,000 ≥ 30,000, so 30x ≥ 45,000 and x ≥ 1,500. Check: 30(1,500) − 15,000 = 30,000. Option 1,501 wrongly treats the condition as strict.
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