3 Men, A, B, and C complete a work in such a way that A works for all the day. B works for 1st and 2nd day and C works for 3rd, 4th and 5th day. If B+C can do as much work in 2 days as A alone does in 3 days. In how many days A, B and C alone do the work If B+C can complete the whole work without the help of A in 6 days?
Answers
Answer:
Step-by-step explanation:
B and C can do as much work in 2 days as A does in 3 days (Given)
∵ B and C finish a work in 6 days (Note: 2 multiplied by 3 = 6)
∴ A alone can finish the work in 9 days ( 3 multiplied by 3)
Let work done by B in one day is x and work done by C in one day is y.
Work done by A in one day = 1/9.
According to the question,
5x/9 + 2x + 3y = 1.
2x + 3y = 1 - 5/9 = 4/9. --------------------------- [1]
Again since B and C can complete the work in 6 days
6x + 6y = 1
x + y = 1/6 --------------------------------------- [2]
Multiplying [2] by 2 and subtracting it from [1],
=> y = 4/9 - 1/3 = 1/9
=> y = 1/9.
=> In 1 day C completes 1/9 days of work
=> C takes 9 days to complete the work.
Putting the value of y in [2],
x = 1/6 - 1/9 = 1/18.
=> In 1 day, B completes 1/18 days of work
=> B takes 18 days to complete the work.
Thus,
A takes 9 days working alone.
B takes 18 days working alone.
C takes 9 days working alone.