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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 B to complete the work independently.
- a)80 days
- b)100 days
- c)120 days
- d)140 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 take X days to complete the work then in one –sixth of the time i.e. x/6 days. Now A do half work as done by B so A will take twice the time i.e. 2*x/6 = x/3 to complete the job alone
So 1/x + 3/x = 1/20, x = 80 days
So 1/x + 3/x = 1/20, x = 80 days
Most Upvoted Answer
A does half as much work as B does in one sixth of the time. If togeth...
If B take 1/6 of the time then A required 1/2 of that time hence A need 1/3 of B
A= 1/3 B
1/A +1/B = 1/20
put value of A
1/(1/3)B + 1/B =. 1/20
3/B +1/B = 1/20
B=80
A= 1/3 B
1/A +1/B = 1/20
put value of A
1/(1/3)B + 1/B =. 1/20
3/B +1/B = 1/20
B=80
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A does half as much work as B does in one sixth of the time. If togeth...
Given:
A does half as much work as B does in one-sixth of the time.
Let's assume that B takes x days to complete the work independently.
Work done by B in one day = 1/x
Work done by A in one day = 1/(2x)
Together, they take 20 days to complete the work.
Work done by B in 20 days = (1/x) * 20 = 20/x
Work done by A in 20 days = (1/(2x)) * 20 = 10/x
Since A does half as much work as B in one-sixth of the time, we have the following equation:
(1/(2x)) * (1/6) = 1/x
Simplifying the equation, we get:
1/(12x) = 1/x
Cross-multiplying, we get:
x = 12x
Dividing both sides by x (assuming x is not equal to 0), we get:
1 = 12
This is not possible, so our assumption that B takes x days to complete the work independently is incorrect.
Therefore, the correct answer is option A) 80 days.
A does half as much work as B does in one-sixth of the time.
Let's assume that B takes x days to complete the work independently.
Work done by B in one day = 1/x
Work done by A in one day = 1/(2x)
Together, they take 20 days to complete the work.
Work done by B in 20 days = (1/x) * 20 = 20/x
Work done by A in 20 days = (1/(2x)) * 20 = 10/x
Since A does half as much work as B in one-sixth of the time, we have the following equation:
(1/(2x)) * (1/6) = 1/x
Simplifying the equation, we get:
1/(12x) = 1/x
Cross-multiplying, we get:
x = 12x
Dividing both sides by x (assuming x is not equal to 0), we get:
1 = 12
This is not possible, so our assumption that B takes x days to complete the work independently is incorrect.
Therefore, the correct answer is option A) 80 days.
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