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A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
- a)10 days
- b)20 days
- c)15 days
- d)11 days
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A and B together can complete a work in 12 days. A alone can complete...
- Work done by A in one day = 1/20. o B's 1 day's work (1/12 - 1/20) = (2/60)= 1/30.
- B's half day work = (1/30)/2 = 1/60
- A and B 's one day work (if B work for half day) = (1/20 + 1/60) = (4/60)= 1/15
- Therefore, total number of days to complete the work = 15 days.
Most Upvoted Answer
A and B together can complete a work in 12 days. A alone can complete...
Given:
A + B = 1/12 ----(1)
A = 1/20
To find:
Number of days A and B together will complete the work if B does the work only for half a day daily.
Solution:
Let us assume that B can finish the work in ‘x’ days.
Therefore, B can finish 1/x of the work in a day.
As B works for only half a day, he will finish 1/2x of the work in a day.
From equation (1), we can write:
1/12 - 1/20 = 1/x - 1/2x
Simplifying this equation, we get:
x = 15
Therefore, B can finish the work in 15 days.
Now, we need to find the number of days A and B together will complete the work.
Let us assume that they take ‘y’ days to complete the work together.
Therefore, in a day, A and B together can finish 1/y of the work.
As A completes 1/20 of the work in a day, B will complete 1/2x of the work in a day.
So, we can write:
1/y = 1/20 + 1/2x
Substituting the value of ‘x’ as 15, we get:
1/y = 1/20 + 1/30
1/y = (3 + 2)/60
1/y = 5/60
y = 12
Therefore, A and B together will complete the work in 12 days.
Hence, the correct option is (c) 15 days.
A + B = 1/12 ----(1)
A = 1/20
To find:
Number of days A and B together will complete the work if B does the work only for half a day daily.
Solution:
Let us assume that B can finish the work in ‘x’ days.
Therefore, B can finish 1/x of the work in a day.
As B works for only half a day, he will finish 1/2x of the work in a day.
From equation (1), we can write:
1/12 - 1/20 = 1/x - 1/2x
Simplifying this equation, we get:
x = 15
Therefore, B can finish the work in 15 days.
Now, we need to find the number of days A and B together will complete the work.
Let us assume that they take ‘y’ days to complete the work together.
Therefore, in a day, A and B together can finish 1/y of the work.
As A completes 1/20 of the work in a day, B will complete 1/2x of the work in a day.
So, we can write:
1/y = 1/20 + 1/2x
Substituting the value of ‘x’ as 15, we get:
1/y = 1/20 + 1/30
1/y = (3 + 2)/60
1/y = 5/60
y = 12
Therefore, A and B together will complete the work in 12 days.
Hence, the correct option is (c) 15 days.
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A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?a) 10 daysb) 20 daysc) 15 daysd) 11 daysCorrect answer is option 'C'. Can you explain this answer?
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