Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
Answer & explanation
Answer: (b) 1/5
From y = kx², k = 50/25 = 2, so y = 98 gives x = 7. From xz = constant = 5 × 7/25 = 7/5, z = (7/5)/7 = 1/5.
- y = kx²: 50 = k × 25, so k = 2.
- y = 98: 2x² = 98, x² = 49, x = 7 (x is positive).
- xz = constant = 5 × 7/25 = 7/5.
- z = (7/5) ÷ 7 = 1/5.
- Check: x rose from 5 to 7, so z must fall in the ratio 5 : 7 — (7/25) × (5/7) = 1/5.
Remember · Direct variation: ratio stays constant; inverse variation: product stays constant. Find each constant from the given pair.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·