Multiple choice

X and Y together finish a piece of work in 30 days. X works for 16 days and Y finishes the remaining work alone in 44 days. In how many days will Y finish the whole work?

  1. 60 days

  2. 46 days

  3. 14 days

  4. 28 days

  5. 37 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let X and Y be the work rates. We have 30(X+Y) = 1, so X+Y = 1/30. Also, 16X + 44Y = 1. Substituting X = 1/30 - Y into the second equation gives 16(1/30 - Y) + 44Y = 1, which simplifies to 16/30 + 28Y = 1, or 28Y = 14/30 = 7/15. Thus Y = 7/(15*28) = 1/60. Y takes 60 days.

AI explanation

Let the total work be the least common multiple of 30 and 44, which is 660 units. The combined efficiency of X and Y is 660 / 30 = 22 units per day. According to the work equation, (16 * 22) + (44 * Y's efficiency) = 660. Solving this gives 352 + 44 * Y's efficiency = 660, so Y's efficiency is 308 / 44 = 7 units per day. Therefore, Y alone can complete the entire work in 660 / 7 = 60 days.

Keep practicing — related questions