2018 · Q44
X and Y together can finish a job in 6 days. X can alone do the same job in 12 days. How long will Y alone take to do the same job ?
Elementary MathematicsTime and Work
- A16 days
- B12 days
- C10 days
- D8 days
Explanation
Let Y take y days alone. Work rates add reciprocally: 1/12 + 1/y = 1/6. Subtracting 1/12 from both sides gives 1/y = 1/6 − 1/12 = 1/12, so y = 12 days. Intuitively, since X alone needs 12 days — twice as slow as the pair's 6 days — Y must contribute exactly as much as X, finishing in the same 12 days. Hence option (B) 12 days.