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A alone can do a piece of work in 20 days, B alone in 40 days and C alone in 60 days. Everyone begin to do the work together, but A leaves after 4 days and B leaves 6 days before the completion of the work. How many days did the work last?
  • a)
    22 days
  • b)
    21 2/5 days
  • c)
    22 4/5 days
  • d)
    25 days
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A alone can do a piece of work in 20 days, B alone in 40 days and C a...
Total work in 1 day by A, B and C = 1/20 + 1/40 + 1/60 = 11/120
In 4 days = 44/120
By C in last 6 days = 6/60 = 1/10
Total = 44/120 + 1/10 = 56/120
Work left = 1 - 56/120 = 64/120
Work done by B and C in one day = 1/40 + 1/60 = 5/120
Work left is done by B and C. Number of days it takes = (64/120)*(120/5) = 64/5
Total time = 10 + 64/5 = 22 4/5
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Most Upvoted Answer
A alone can do a piece of work in 20 days, B alone in 40 days and C a...
Given:
A can do the work in 20 days,
B can do the work in 40 days,
C can do the work in 60 days.

Let us assume that the total work is 120 units (LCM of 20, 40, and 60).

So, A can do 6 units of work in a day (120/20),
B can do 3 units of work in a day (120/40),
C can do 2 units of work in a day (120/60).

Let us assume that everyone works for 'd' days.

Total work done by A, B, and C in 'd' days = (6 + 3 + 2) d = 11d

After 4 days, A leaves the work. So, the work done by A in 4 days = 4 x 6 = 24 units.

Remaining work = 120 - 24 = 96 units.

B leaves the work 6 days before the completion of the work. So, the work done by B in (d-6) days = (3 x (d-6)) = 3d - 18 units.

Total work done by A and B = 24 + (3d - 18) = 3d + 6 units.

Work done by C in 'd' days = 2d units.

Total work done by A, B, and C in 'd' days = 11d units.

So, 11d = 3d + 6 + 2d
=> 6d = 6
=> d = 1

Therefore, the work lasted for 4 + 1 + 6 = 11 days.

But the answer is given in mixed fraction form, so we need to convert the answer to mixed fraction.

11 days = 11/1 days = 55/5 days = 22/5 days.

Hence, the correct answer is option (c) 22 4/5 days.
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A alone can do a piece of work in 20 days, B alone in 40 days and C alone in 60 days. Everyone begin to do the work together, but A leaves after 4 days and B leaves 6 days before the completion of the work. How many days did the work last?a)22 daysb)21 2/5 daysc)22 4/5 daysd)25 daysCorrect answer is option 'C'. Can you explain this answer?
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