Railways Exam  >  Railways Questions  >   A alone can do a piece of work in 20 days, B... Start Learning for Free
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 ⅘
View all questions of this test
Most Upvoted Answer
A alone can do a piece of work in 20 days, B alone in 40 days and C a...
To solve this problem, we can calculate the rates at which A, B, and C can complete the work individually and then combine their rates to find the rate at which they work together. We can then use this combined rate to determine the total time taken to complete the work.

Given:
A can complete the work in 20 days.
B can complete the work in 40 days.
C can complete the work in 60 days.

Calculating individual rates:
Let's assume that A's rate of work is "x" units per day.
So, A can complete the work in 20 days, which means in 1 day, A can complete 1/20th of the work.
Therefore, A's rate of work is x = 1/20 units per day.

Similarly, for B and C:
B's rate of work is y = 1/40 units per day.
C's rate of work is z = 1/60 units per day.

Combining the rates:
The combined rate at which A, B, and C work together is the sum of their individual rates.
Combined rate (x + y + z) = 1/20 + 1/40 + 1/60

Finding a common denominator:
To add these fractions, we need to find a common denominator.
The common denominator for 20, 40, and 60 is 120.
So, let's rewrite the fractions with the common denominator:
Combined rate (x + y + z) = (6/120) + (3/120) + (2/120)
Combined rate (x + y + z) = 11/120 units per day

Finding the total time taken:
Let's assume that the total time taken to complete the work is "t" days.
In the given scenario, A works for 4 days and B works for (t - 6) days.
Using the combined rate, we can express the work done by A and B as:
Work done by A = (x * 4) = (4/20) = 1/5 of the total work
Work done by B = (y * (t - 6)) = ((t - 6)/40) of the total work

Since they all work together, the sum of their work should equal the total work:
1/5 + (t - 6)/40 + (1 - 1/5 - (t - 6)/40) = 1

Simplifying the equation:
Multiplying through by 40 to remove the denominators:
8 + 2(t - 6) + 40 - 8 - t + 6 = 40
8 + 2t - 12 + 40 - 8 - t + 6 = 40
t = 22

Therefore, the work lasted for 22 days.
Hence, the correct answer is option C) 22 4/5 days.
Explore Courses for Railways exam

Similar Railways Doubts

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?
Question Description
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? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about 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? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Railways. Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice Railways tests.
Explore Courses for Railways exam

Top Courses for Railways

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev