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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B on odd days and C on even days?
- a)7 days
- b)8 days
- c)9 days
- d)10 days
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A, B and C can do a piece of work in 11 days, 20 days and 55 days resp...
(A+B)'s 1 day' s work = (1/11 + 1/20 ) = 31/220
(A+C)'s 1 day's work = ( 1/11 + 1/55) = 6/55
Work done in 2 days by them= ( 31/220 + 6/55) = 55/220 = %.
Therefore, Whole work will be done in 8 days
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Community Answer
A, B and C can do a piece of work in 11 days, 20 days and 55 days resp...
Given information:
A can do the work in 11 days.
B can do the work in 20 days.
C can do the work in 55 days.
Approach:
To find the time taken to complete the work when A is assisted by B on odd days and C on even days, we can break down the work into smaller parts based on the number of days.
Calculation:
Let's assume the total work done is 220 units (LCM of 11, 20, and 55).
Work done by A:
A can complete the work in 11 days, so the work done by A in one day = 220/11 = 20 units.
Work done by B:
B can complete the work in 20 days, so the work done by B in one day = 220/20 = 11 units.
Work done by C:
C can complete the work in 55 days, so the work done by C in one day = 220/55 = 4 units.
Work done on odd days:
On odd days, A is assisted by B. Since A can do 20 units of work in one day and B can do 11 units of work in one day, the total work done on odd days = 20 + 11 = 31 units.
Work done on even days:
On even days, A is assisted by C. Since A can do 20 units of work in one day and C can do 4 units of work in one day, the total work done on even days = 20 + 4 = 24 units.
Time taken to complete the work:
Now, we need to find the number of odd and even days required to complete the work.
Let's assume the work is completed in 'x' odd days and 'y' even days.
Total work done in 'x' odd days = 31x units.
Total work done in 'y' even days = 24y units.
The sum of odd and even days should add up to the total work i.e., 31x + 24y = 220.
Since x and y are positive integers, we can solve this equation to find the values of x and y that satisfy the equation.
The possible values of x and y that satisfy the equation are:
x = 7 and y = 2, or
x = 15 and y = 5, or
x = 23 and y = 8.
Among these options, the minimum time taken to complete the work is when x = 7 and y = 2, which is 7 + 2 = 9 days.
Therefore, the work can be done in 9 days when A is assisted by B on odd days and C on even days.
Hence, the correct answer is option C) 9 days.
A can do the work in 11 days.
B can do the work in 20 days.
C can do the work in 55 days.
Approach:
To find the time taken to complete the work when A is assisted by B on odd days and C on even days, we can break down the work into smaller parts based on the number of days.
Calculation:
Let's assume the total work done is 220 units (LCM of 11, 20, and 55).
Work done by A:
A can complete the work in 11 days, so the work done by A in one day = 220/11 = 20 units.
Work done by B:
B can complete the work in 20 days, so the work done by B in one day = 220/20 = 11 units.
Work done by C:
C can complete the work in 55 days, so the work done by C in one day = 220/55 = 4 units.
Work done on odd days:
On odd days, A is assisted by B. Since A can do 20 units of work in one day and B can do 11 units of work in one day, the total work done on odd days = 20 + 11 = 31 units.
Work done on even days:
On even days, A is assisted by C. Since A can do 20 units of work in one day and C can do 4 units of work in one day, the total work done on even days = 20 + 4 = 24 units.
Time taken to complete the work:
Now, we need to find the number of odd and even days required to complete the work.
Let's assume the work is completed in 'x' odd days and 'y' even days.
Total work done in 'x' odd days = 31x units.
Total work done in 'y' even days = 24y units.
The sum of odd and even days should add up to the total work i.e., 31x + 24y = 220.
Since x and y are positive integers, we can solve this equation to find the values of x and y that satisfy the equation.
The possible values of x and y that satisfy the equation are:
x = 7 and y = 2, or
x = 15 and y = 5, or
x = 23 and y = 8.
Among these options, the minimum time taken to complete the work is when x = 7 and y = 2, which is 7 + 2 = 9 days.
Therefore, the work can be done in 9 days when A is assisted by B on odd days and C on even days.
Hence, the correct answer is option C) 9 days.
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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B on odd days and C on even days?a)7 daysb)8 daysc)9 daysd)10 daysCorrect answer is option 'B'. Can you explain this answer?
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