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A, B and C can alone complete a work in 10, 12 and 15 days respectively. All started the work but B left the work 3 days before completion. How much work was then done by A and B together in the total work?
- a)2/3
- b)3/4
- c)1/3
- d)3/5
- e)2/5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A, B and C can alone complete a work in 10, 12 and 15 days respectivel...
Let work completed in x days, so A and C worked for all x days, and B for (x-3) days.
So
(1/10 + 1/15)*x + (1/12)*(x-3) = 1
Solve, x = 5 days
In 5 days, A did 5/10 = 1/2 of work
In (5-3) = 2 days, B did 2/12 = 1/6 of work
So total by A and B = (1/2 + 1/6) = 2/3
So
(1/10 + 1/15)*x + (1/12)*(x-3) = 1
Solve, x = 5 days
In 5 days, A did 5/10 = 1/2 of work
In (5-3) = 2 days, B did 2/12 = 1/6 of work
So total by A and B = (1/2 + 1/6) = 2/3
Most Upvoted Answer
A, B and C can alone complete a work in 10, 12 and 15 days respectivel...
Given information:
A can complete the work in 10 days.
B can complete the work in 12 days.
C can complete the work in 15 days.
B left the work 3 days before completion.
To find:
How much work was then done by A and B together in the total work?
Solution:
To solve this problem, we need to understand the concept of work done per day.
Let's assume that the total work to be done is 60 units (considering the LCM of 10, 12, and 15).
Work done by A per day:
A can complete the work in 10 days, so the work done by A per day is 60/10 = 6 units.
Work done by B per day:
B can complete the work in 12 days, so the work done by B per day is 60/12 = 5 units.
Work done by C per day:
C can complete the work in 15 days, so the work done by C per day is 60/15 = 4 units.
Now, let's calculate the total work done by A, B, and C in the given time frame.
Work done by A in the given time:
Since A is working continuously until the completion of the work, the work done by A in the given time is 6 units/day * (10-3) days = 6 * 7 = 42 units.
Work done by B in the given time:
B left the work 3 days before completion, so the work done by B in the given time is 5 units/day * 3 days = 15 units.
Total work done by A and B together:
The total work done by A and B together in the given time is 42 units + 15 units = 57 units.
Calculating the fraction of work done:
To find the fraction of work done by A and B together, we need to divide the total work done by A and B by the total work done.
Fraction of work done by A and B = (57 units) / (60 units) = 19/20 = 0.95
This can be simplified to 2/3.
Therefore, the answer is option 'A' (2/3).
A can complete the work in 10 days.
B can complete the work in 12 days.
C can complete the work in 15 days.
B left the work 3 days before completion.
To find:
How much work was then done by A and B together in the total work?
Solution:
To solve this problem, we need to understand the concept of work done per day.
Let's assume that the total work to be done is 60 units (considering the LCM of 10, 12, and 15).
Work done by A per day:
A can complete the work in 10 days, so the work done by A per day is 60/10 = 6 units.
Work done by B per day:
B can complete the work in 12 days, so the work done by B per day is 60/12 = 5 units.
Work done by C per day:
C can complete the work in 15 days, so the work done by C per day is 60/15 = 4 units.
Now, let's calculate the total work done by A, B, and C in the given time frame.
Work done by A in the given time:
Since A is working continuously until the completion of the work, the work done by A in the given time is 6 units/day * (10-3) days = 6 * 7 = 42 units.
Work done by B in the given time:
B left the work 3 days before completion, so the work done by B in the given time is 5 units/day * 3 days = 15 units.
Total work done by A and B together:
The total work done by A and B together in the given time is 42 units + 15 units = 57 units.
Calculating the fraction of work done:
To find the fraction of work done by A and B together, we need to divide the total work done by A and B by the total work done.
Fraction of work done by A and B = (57 units) / (60 units) = 19/20 = 0.95
This can be simplified to 2/3.
Therefore, the answer is option 'A' (2/3).
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Community Answer
A, B and C can alone complete a work in 10, 12 and 15 days respectivel...
Let work completed in x days, so A and C worked for all x days, and B for (x-3) days.
So
(1/10 + 1/15)*x + (1/12)*(x-3) = 1
Solve, x = 5 days
In 5 days, A did 5/10 = 1/2 of work
In (5-3) = 2 days, B did 2/12 = 1/6 of work
So total by A and B = (1/2 + 1/6) = 2/3
So
(1/10 + 1/15)*x + (1/12)*(x-3) = 1
Solve, x = 5 days
In 5 days, A did 5/10 = 1/2 of work
In (5-3) = 2 days, B did 2/12 = 1/6 of work
So total by A and B = (1/2 + 1/6) = 2/3
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