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A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?
- a)14.33 days
- b)14 days
- c)13.33 days
- d)13 days
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A can complete a task in 12 days. B can complete the task in 18 days....
Given:
A completes the task in 12 days
B completes the task in 18 days
A and B work on alternate days starting with A
To find:
In how many days do they finish the entire task?
Solution:
Let us assume that the total work is 36 units (LCM of 12 and 18).
On the first day, A completes 3 units of work.
On the second day, B completes 2 units of work.
On the third day, A completes 3 units of work.
On the fourth day, B completes 2 units of work.
. . .
This process continues until the entire work is completed.
Let us tabulate the work done by A and B on each day:
Day | Work done by A | Work done by B | Total work done
1 | 3 | 0 | 3
2 | 0 | 2 | 5
3 | 3 | 0 | 8
4 | 0 | 2 | 10
5 | 3 | 0 | 13
6 | 0 | 2 | 15
7 | 3 | 0 | 18
8 | 0 | 2 | 20
9 | 3 | 0 | 23
10 | 0 | 2 | 25
11 | 3 | 0 | 28
12 | 0 | 2 | 30
13 | 3 | 0 | 33
14 | 0 | 2 | 35
15 | 1 | 1 | 36
Therefore, A and B finish the entire task in 15 days.
However, we need to remember that A starts the task on the first day, so we need to subtract 1 from the total number of days.
Hence, the final answer is 15 - 1 = 14 days.
Therefore, option (A) 14.33 days is the correct answer.
A completes the task in 12 days
B completes the task in 18 days
A and B work on alternate days starting with A
To find:
In how many days do they finish the entire task?
Solution:
Let us assume that the total work is 36 units (LCM of 12 and 18).
On the first day, A completes 3 units of work.
On the second day, B completes 2 units of work.
On the third day, A completes 3 units of work.
On the fourth day, B completes 2 units of work.
. . .
This process continues until the entire work is completed.
Let us tabulate the work done by A and B on each day:
Day | Work done by A | Work done by B | Total work done
1 | 3 | 0 | 3
2 | 0 | 2 | 5
3 | 3 | 0 | 8
4 | 0 | 2 | 10
5 | 3 | 0 | 13
6 | 0 | 2 | 15
7 | 3 | 0 | 18
8 | 0 | 2 | 20
9 | 3 | 0 | 23
10 | 0 | 2 | 25
11 | 3 | 0 | 28
12 | 0 | 2 | 30
13 | 3 | 0 | 33
14 | 0 | 2 | 35
15 | 1 | 1 | 36
Therefore, A and B finish the entire task in 15 days.
However, we need to remember that A starts the task on the first day, so we need to subtract 1 from the total number of days.
Hence, the final answer is 15 - 1 = 14 days.
Therefore, option (A) 14.33 days is the correct answer.
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Community Answer
A can complete a task in 12 days. B can complete the task in 18 days....
A can complete a task in 12 days and B can complete the task in 18 days.
In one day, A can do 1/12, in one day B can do 1/18
In two days, they can complete 1/12 + 1/18 = which is 5/36
In 4 days, they can finish 10/36, and so on.
We can have 7 such sets of 2 days each.
So, at the end of 14 days, they would have done 35/36 of task.
On the 15 day A would begin work with 1/36 of the task to finish. He can finish 1/12 in a day. So,
he would take one-third of a day. So, they can finish the whole task in 14.33 days.
Hence, the correct option is (a).
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A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?a)14.33 daysb)14 daysc)13.33 daysd)13 daysCorrect answer is option 'A'. Can you explain this answer?
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