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CA Foundation · Quantitative Aptitude · Linear Inequalities

A retailer stocks notebooks and pens. Each notebook costs ₹20 and each pen costs ₹5. The retailer has ₹1,000 to spend and wants to stock at least twice as many pens as notebooks. If n is the number of notebooks and p is the number of pens, identify which system of inequalities is correct.

The correct system is 20n + 5p ≤ 1,000 (budget constraint with 'not exceeding' ₹1,000) and p ≥ 2n (at least twice as many pens as notebooks). Cost values must be included in the budget inequality, and the quantity relationship must preserve its direction.

  1. A20n + 5p ≤ 1,000 and p ≥ 2nCorrect
  2. B20n + 5p ≤ 1,000 and p ≤ 2n
  3. C20n + 5p ≥ 1,000 and p ≥ 2n
  4. D20n + 5p = 1,000 and 2p ≥ n

Explanation

The budget constraint is that total cost does not exceed ₹1,000: 20n + 5p ≤ 1,000. 'At least twice as many pens as notebooks' means p ≥ 2n. Option (2) uses ≤ for the quantity condition (incorrect direction). Option (3) uses ≥ for budget (should be ≤). Option (4) uses equality for budget and reverses the quantity relationship.

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