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If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?
- a)60
- b)45
- c)40
- d)30
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If A and B together can complete a piece of work in 15 days and B alon...
1st method:
A and B complete a work in = 15 days
One day's work of (A + B) = 1/ 15
A and B complete a work in = 15 days
One day's work of (A + B) = 1/ 15
B complete the work in = 20 days;
One day's work of B = 1/20
One day's work of B = 1/20
Then, A's one day's work
=1/15−1/20
=(4−3)/6
=1/60
=(4−3)/6
=1/60
Thus, A can complete the work in = 60 days.
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Community Answer
If A and B together can complete a piece of work in 15 days and B alon...
Given:
A+B can complete a piece of work in 15 days
B alone can complete the same work in 20 days
To find:
In how many days can A alone complete the work?
Solution:
Let's assume that the total work is 60 units (LCM of 15 and 20).
So, A+B can complete 4 units of work per day (60/15) and B alone can complete 3 units of work per day (60/20).
Let's say A alone can complete x units of work per day.
So, A+B can complete (4x) units of work in a day.
Now, according to the given information:
A+B can complete 4 units of work per day.
So, A+B completes (4*15) = 60 units of work in 15 days.
Also, we know that B alone can complete the same work in 20 days.
So, B can complete (3*20) = 60 units of work in 20 days.
Using the above information, we can calculate A's work efficiency as follows:
A+B can complete 60 units of work in 15 days.
So, (4x)*15 = 60
=> 4x = 4
=> x = 1
Therefore, A alone can complete 1 unit of work per day.
Hence, A can complete the entire work of 60 units in 60 days.
Therefore, the correct answer is option A) 60.
A+B can complete a piece of work in 15 days
B alone can complete the same work in 20 days
To find:
In how many days can A alone complete the work?
Solution:
Let's assume that the total work is 60 units (LCM of 15 and 20).
So, A+B can complete 4 units of work per day (60/15) and B alone can complete 3 units of work per day (60/20).
Let's say A alone can complete x units of work per day.
So, A+B can complete (4x) units of work in a day.
Now, according to the given information:
A+B can complete 4 units of work per day.
So, A+B completes (4*15) = 60 units of work in 15 days.
Also, we know that B alone can complete the same work in 20 days.
So, B can complete (3*20) = 60 units of work in 20 days.
Using the above information, we can calculate A's work efficiency as follows:
A+B can complete 60 units of work in 15 days.
So, (4x)*15 = 60
=> 4x = 4
=> x = 1
Therefore, A alone can complete 1 unit of work per day.
Hence, A can complete the entire work of 60 units in 60 days.
Therefore, the correct answer is option A) 60.
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