CA Foundation · Quantitative Aptitude · Linear Inequalities
A jeweller has ₹50,000 to invest. She allocates amount x to gold and amount y to silver such that the investment in gold is at least ₹5,000 more than the investment in silver, and the total must equal ₹50,000. Which pair of conditions correctly represents this situation?
The situation requires two conditions: the total investment x + y = 50,000 (equality) and gold investment being at least ₹5,000 more than silver, written as x ≥ y + 5,000. This correctly captures both the budget constraint and the comparative allocation rule.
- Ax + y = 50,000 and x ≥ y + 5,000Correct
- Bx + y = 50,000 and x ≥ 5,000
- Cx + y = 50,000 and x + y ≥ 55,000
- Dx + y = 50,000 and x − y ≤ 5,000
Explanation
Total investment is fixed at ₹50,000, so x + y = 50,000 (equality, not inequality). The condition 'gold is at least ₹5,000 more than silver' means x ≥ y + 5,000. Option (2) ignores the comparison between x and y. Option (3) contradicts the total. Option (4) reverses the inequality direction.
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