Multiple choice

Horrik and Ecbert can together plough a field in 60 days. They worked together for 40 days and then, Ecbert left the task. After another 40 days, Horrik completed the remaining task. Horrik alone complete the task in how many days?

  1. 100 days

  2. 96 days

  3. 120 days

  4. 108 days

  5. 80 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let H and E be the work rates. (H+E)*60 = 1. (H+E)*40 + H*40 = 1. 40H + 40E + 40H = 1 -> 80H + 40E = 1. Since E = 1/60 - H, 80H + 40(1/60 - H) = 1. 80H + 2/3 - 40H = 1. 40H = 1/3. H = 1/120. Horrik takes 120 days.

AI explanation

Let the total work be the least common multiple of the given days, which is 60 units. Horrik and Ecbert's combined efficiency is 1 unit per day, so in 40 days they complete 40 units. The remaining 20 units are completed by Horrik alone in 40 days. By the time and work formula, Horrik's efficiency is 20 divided by 40, or 0.5 units per day, meaning Horrik alone takes 60 divided by 0.5 days to complete the task. Horrik alone complete the task in 120 days.

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