Multiple choice

A is thrice as efficient as B and B is twice as efficient as C. if A, B and C work together , how long will they take to complete a job which B complete in $10$ days ?

  1. $\displaystyle \frac{20}{9}$ days
  2. $\displaystyle \frac{11}{9}$ days
  3. $3$ days

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A=3B, B=2C. So A=6C, B=2C. If B takes 10 days, the total work is 10 * B's rate. A+B+C rate = 6C + 2C + C = 9C. B's rate = 2C. Total work = 10 * 2C = 20C. Time = 20C / 9C = 20/9 days.

AI explanation

Since B completes the work in 10 days, let us assume the total work is 10 units, making B's efficiency 1 unit per day. Given A is thrice as efficient as B and B is twice as efficient as C, the efficiencies of A and C are 3 units per day and 0.5 units per day respectively. Working together, their combined efficiency is 4.5 units per day, so the time taken to complete the 10 units of work is 10 divided by 4.5, which equals 20/9 days.

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