Multiple choice

Time taken by A to finish a piece of work is twice the time taken B and thrice thetime taken by C. If all three of them work together, it takes them 2 days to complete theentire work. How much work was done by B alone?

  1. 2 days

  2. 6 days

  3. 3 days

  4. 5 days

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let time for B be x. Then A = 2x, C = 2x/3. Combined rate: 1/(2x) + 1/x + 3/(2x) = 1/2. (1+2+3)/(2x) = 1/2. 6/(2x) = 1/2. 3/x = 1/2, so x = 6. B takes 6 days.

AI explanation

Let the time taken by A be 6x days, so the times taken by B and C are 3x and 2x days respectively. Their work rates are 1/(6x), 1/(3x), and 1/(2x), and working together their combined rate is 1/(6x) + 1/(3x) + 1/(2x) = 1/x. Since they complete the work in 2 days together, 1/x = 1/2, which means x = 2; therefore, B alone takes 3x = 6 days.

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