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CA Foundation · Quantitative Aptitude · Linear Inequalities

A shop sells two types of bags, A at ₹300 and B at ₹200 per bag. The owner wants total sales of at least ₹6,000 from x bags of A and y bags of B. Which inequality represents this condition, and does (10, 15) satisfy it?

The condition is 300x + 200y ≥ 6000, and the point (10, 15) satisfies it. Sales are 3000 + 3000 = ₹6,000, which equals the minimum required, and a non-strict inequality permits equality.

  1. A300x + 200y ≥ 6000; yes, since the sales are ₹6,000Correct
  2. B300x + 200y ≥ 6000; no, since the sales are below ₹6,000
  3. C300x + 200y ≤ 6000; yes, since the sales are ₹6,000
  4. D200x + 300y ≥ 6000; yes, since the sales are ₹6,500

Explanation

At least ₹6,000 gives 300x + 200y ≥ 6000. For (10, 15): 3000 + 3000 = 6000, which meets the condition with equality, so the point is allowed. Option 3 reverses the sign. Option 4 swaps the prices.

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