Multiple choice

Shashi took twice as much time as shishu & thrice as much time as shisham to complete a certain work. If they can finish the work in 4 days when working together, then what will be the time taken by shishu to complete the work alone?

  1. 12 days

  2. 8 days

  3. 24 days

  4. 16 days

  5. None of the above
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A Correct answer
Explanation

Let Shashi's time be T. Shishu's time = T/2. Shisham's time = T/3. Work rates: 1/T + 2/T + 3/T = 1/4. 6/T = 1/4, so T = 24. Shishu's time = 24/2 = 12 days.

AI explanation

By the chain rule for time and work, if Shashi takes twice as much time as Shishu, their efficiency ratio is 1 to 2, and if Shashi takes thrice as much time as Shisham, their efficiency ratio is 1 to 3. Combining these, the efficiency ratio of Shashi, Shishu, and Shisham is 1 to 2 to 3. Their combined efficiency is 6 units per day, so working together for 4 days they complete 24 units of work. Since Shishu's efficiency is 2 units per day, the time taken by Shishu to complete the 24 units alone is 24 divided by 2, which equals 12 days.

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