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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 begins 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

Approach:
- Let the total work be represented by LCM(20, 40, 60) = 120 units.
- Let's consider the rate of work of A, B, and C as a, b, and c respectively. So,
- A can complete 1 unit of work in 20 days, so a = 1/20 units/day.
- B can complete 1 unit of work in 40 days, so b = 1/40 units/day.
- C can complete 1 unit of work in 60 days, so c = 1/60 units/day.

Calculation:
- Let's assume the work lasted for x days.
- In the first 4 days, the work done by A = 4 * a = 4/20 = 1/5 units.
- After 4 days, A leaves and only B and C continue the work.
- In x - 4 days, B and C together complete the remaining work of 1 - 1/5 = 4/5 units.
- The rate at which B and C together complete the work = b + c = 1/40 + 1/60 = 1/24 units/day.
- So, the work done by B and C together in x - 4 days = (x - 4) * (1/24) = (x - 4)/24 units.
- According to the given condition, B leaves 6 days before the completion of the work.
- So, the work done by B alone in 6 days = 6 * b = 6/40 = 3/20 units.
- The remaining work done by C alone = 4/5 - 3/20 = 16/20 - 3/20 = 13/20 units.
- The time taken by C to complete 13/20 units of work = (13/20) / (1/60) = (13/20) * (60/1) = 39 days.
- The total time taken to complete the work = 4 + (x - 4) + 6 + 39 = x + 45.
- According to the given condition, the total time taken to complete the work is equal to 120 days.
- So, x + 45 = 120.
- Solving this equation, we get x = 75.

Therefore, the work lasted for 75 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 begins 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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