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A and B can do a piece of work in 10 days and A alone can do it in 15 days. In how many days can B alone do it?
- a)5 days
- b)6 days
- c)25 days
- d)30 days
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A and B can do a piece of work in 10 days and A alone can do it in 15 ...
Total time taken by A and B together to finish the work = 10 days
And time taken by A alone to finish the work = 15 days
∴ A and B together can do 1/10 of the work in one day and A can do 1/15 of the work in a day.
Work done by B in one day
So, B takes 30 days to do the work alone.
And time taken by A alone to finish the work = 15 days
∴ A and B together can do 1/10 of the work in one day and A can do 1/15 of the work in a day.
Work done by B in one day
So, B takes 30 days to do the work alone.
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Community Answer
A and B can do a piece of work in 10 days and A alone can do it in 15 ...
Let's assume that the total work is represented by W.
A and B together can complete the work in 10 days, so their combined work rate is 1/10 (1 work done in 10 days).
Now, let's consider A's work rate. A can complete the work alone in 15 days, so his work rate is 1/15 (1 work done in 15 days).
To find B's work rate, we subtract A's work rate from the combined work rate of A and B.
B's work rate = Combined work rate of A and B - A's work rate
= 1/10 - 1/15
= (3/30) - (2/30)
= 1/30
This means that B can complete 1/30th of the work in a day.
Now, to find the number of days it will take for B to complete the entire work alone, we can use the formula:
Number of days = Total work / Work rate
= W / (1/30)
= 30W
Therefore, B alone can complete the work in 30 days.
Hence, the correct answer is option D) 30 days.
A and B together can complete the work in 10 days, so their combined work rate is 1/10 (1 work done in 10 days).
Now, let's consider A's work rate. A can complete the work alone in 15 days, so his work rate is 1/15 (1 work done in 15 days).
To find B's work rate, we subtract A's work rate from the combined work rate of A and B.
B's work rate = Combined work rate of A and B - A's work rate
= 1/10 - 1/15
= (3/30) - (2/30)
= 1/30
This means that B can complete 1/30th of the work in a day.
Now, to find the number of days it will take for B to complete the entire work alone, we can use the formula:
Number of days = Total work / Work rate
= W / (1/30)
= 30W
Therefore, B alone can complete the work in 30 days.
Hence, the correct answer is option D) 30 days.
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