Multiple choice

Raju and Dev together can do a piece of work in 10 days. Dev and Sharon can do the same piece of work in 12 days whereas Sharon and Raju can complete it in 15 days. If all the three boys work together, how many days will they take to complete the work?

  1. 4 days

  2. 5 days

  3. 6 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R, D, S be rates. R+D = 1/10, D+S = 1/12, S+R = 1/15. 2(R+D+S) = 1/10 + 1/12 + 1/15 = (6+5+4)/60 = 15/60 = 1/4. R+D+S = 1/8. Time = 8 days.

AI explanation

Let the total work be 60 units, making the combined efficiencies of Raju and Dev 6 units per day, Dev and Sharon 5 units per day, and Sharon and Raju 4 units per day. Adding these three equations gives twice the sum of their individual efficiencies equal to 15 units per day, meaning their combined efficiency is 7.5 units per day. The time they take to complete the 60 units of work together is 60 divided by 7.5, which equals 8 days.

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