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A does half as much work as B in one sixth of the time. If together they take 10 days to complete a work, how much time shall B take to do it alone?
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- 70 days
- 30 days
- 40 days
- 50 days
Correct Option: C
Let B does the whole work in x days
| ∴ Work done by B in 1 day | x |
According to question
| A does the | work in | days | ||
| 2 | 6 |
| ∴ A does the whole work in | 6 |
| or = | days | 3 |
| ∴ Work done by A in one day = | x |
∴ Work done by A and B together in one day
| = | + | = | ||||
| x | x | x |
∴ Time taken to complete the whole work by A and B together
| = | = | days | ||
| 4/x | 4 |
Again, given that
| = 10 | 4 |
∴ x = 40 days
Aliter : Using Rule 22,
Here, n = 3, d = 10
∵ A is 3 times more efficient thanB.
Time taken by B = (n + 1) × D
= (3 + 1) × 10
= 40 days
