Direct & Inverse Variation

Two quantities vary directly when their ratio stays constant: y ∝ x means y = kx, so doubling x doubles y (think cost vs quantity bought, or distance vs time at fixed speed). They vary inversely when their product stays constant: y ∝ 1/x means xy = k, so doubling x halves y (think men vs days to finish a fixed job, or speed vs time over a fixed distance). The fastest CAT method is to set up the constant once and reuse it: for direct variation use y1/x1 = y2/x2; for inverse use x1·y1 = x2·y2. Many questions combine both — for example, work done ∝ (men × days), so men and days are inversely related for a fixed amount of work. The classic trap is treating an inverse relationship as direct: more men should mean FEWER days, not more, so the answer must move the opposite way.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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