2018 · Q10
Two workers ‘A’ and ‘B’ working together completed a job in 5 days. Had ‘A’ worked twice as efficiently as he actually did and ‘B’ worked one-third as efficiently as he actually did, the work would have completed in 3 days. In how many days could ‘A’ alone complete the job?
Elementary MathematicsTime and Work
- A3 1/2
- B4 1/6
- C5 1/2
- D6 1/4
Explanation
Let a and b be the daily work rates of A and B. Then a + b = 1/5 and 2a + b/3 = 1/3. Eliminating b: 2a + (1/5 - a)/3 = 1/3, which simplifies to (5/3)a = 4/15, so a = 4/25. A alone therefore takes 25/4 = 6 1/4 days. Hence option D.