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A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.
- a)80/3 days
- b)100/3 days
- c)60/3 days
- d)140/3 days
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A does half as much work as B does in one sixth of the time. If togeth...
Let B complete the work in X days so in one day work done by B is 1/x
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days
Most Upvoted Answer
A does half as much work as B does in one sixth of the time. If togeth...
Given:
Work done by A in 1/6th of the time taken by B = 1/2
Let us assume that B takes x days to complete the work independently.
So, work done by B in 1 day = 1/x
Also, work done by A in the same time = 1/(2x/6) = 3/x
Now, let us consider their combined work rate per day as M.
So, M = 1/x + 3/x = 4/x
And, the total work done by both of them in 1 day = 1/20
So, 4/x = 1/20
x = 80/4 = 20
So, B takes 20 days to complete the work.
Now, let us find the time taken by A to complete the work independently.
We know that A does half the work of B in 1/6th of his time. So, let us assume that A takes y days to complete the work independently.
So, work done by A in 1 day = 1/y
Work done by B in y days = 1
Work done by A in (y/6) days = 1/2
Now, using the formula of work done = rate x time, we can equate the work done by A in y days and in (y/6) days.
1/y = (1/2)/(y/6)
1/y = 3/y
y = 3
So, A takes 3 days to complete the work independently.
Hence, the answer is option A) 80/3 days.
Work done by A in 1/6th of the time taken by B = 1/2
Let us assume that B takes x days to complete the work independently.
So, work done by B in 1 day = 1/x
Also, work done by A in the same time = 1/(2x/6) = 3/x
Now, let us consider their combined work rate per day as M.
So, M = 1/x + 3/x = 4/x
And, the total work done by both of them in 1 day = 1/20
So, 4/x = 1/20
x = 80/4 = 20
So, B takes 20 days to complete the work.
Now, let us find the time taken by A to complete the work independently.
We know that A does half the work of B in 1/6th of his time. So, let us assume that A takes y days to complete the work independently.
So, work done by A in 1 day = 1/y
Work done by B in y days = 1
Work done by A in (y/6) days = 1/2
Now, using the formula of work done = rate x time, we can equate the work done by A in y days and in (y/6) days.
1/y = (1/2)/(y/6)
1/y = 3/y
y = 3
So, A takes 3 days to complete the work independently.
Hence, the answer is option A) 80/3 days.
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