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X alone takes 5 days and Y alone takes 7 days to finish a job. How many days will X and Y take to finish the job working on alternate days starting with X?
- a)5 + 1/5
- b)5 + 2/5
- c)5 + 3/5
- d)5 + 4/5
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
X alone takes 5 days and Y alone takes 7 days to finish a job. How man...
Let the total work be LCM of number of days taken by X and Y individually.
Total work = LCM (5, 7) = 35 unit
In 2 days, X & Y will complete (12/35)th of the total work.
In this manner they will complete (24/35)th work in 4 days.
After this X will work for 1 day and he completes 1/5th work.
After 5th day, work left = (11/35 - 1/5) = 4/35 On 6th day, Y will do the remaining 4/35th work in 4/5th of days time.
So total time taken is 5 + 4/5 days.
Hence, option 4.
In this manner they will complete (24/35)th work in 4 days.
After this X will work for 1 day and he completes 1/5th work.
After 5th day, work left = (11/35 - 1/5) = 4/35 On 6th day, Y will do the remaining 4/35th work in 4/5th of days time.
So total time taken is 5 + 4/5 days.
Hence, option 4.
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Community Answer
X alone takes 5 days and Y alone takes 7 days to finish a job. How man...
To find the number of days X and Y will take to finish the job working on alternate days starting with X, we can use the concept of work rate.
Let's assume that the total work is 1 unit.
Work rate of X: X completes 1/5 of the job in 1 day.
Work rate of Y: Y completes 1/7 of the job in 1 day.
Since they are working on alternate days, X will work on odd-numbered days and Y will work on even-numbered days.
On Day 1, X completes 1/5 of the job.
On Day 2, Y completes 1/7 of the remaining job (4/5).
On Day 3, X completes 1/5 of the remaining job (3/5).
On Day 4, Y completes 1/7 of the remaining job (2/5).
On Day 5, X completes 1/5 of the remaining job (1/5).
At this point, there is only 1/5 of the job remaining, which X completes on Day 6.
Therefore, X and Y together will take 5 days and 4/5 of the 6th day to finish the job.
So, the correct answer is option 'D': 5 4/5.
Let's assume that the total work is 1 unit.
Work rate of X: X completes 1/5 of the job in 1 day.
Work rate of Y: Y completes 1/7 of the job in 1 day.
Since they are working on alternate days, X will work on odd-numbered days and Y will work on even-numbered days.
On Day 1, X completes 1/5 of the job.
On Day 2, Y completes 1/7 of the remaining job (4/5).
On Day 3, X completes 1/5 of the remaining job (3/5).
On Day 4, Y completes 1/7 of the remaining job (2/5).
On Day 5, X completes 1/5 of the remaining job (1/5).
At this point, there is only 1/5 of the job remaining, which X completes on Day 6.
Therefore, X and Y together will take 5 days and 4/5 of the 6th day to finish the job.
So, the correct answer is option 'D': 5 4/5.
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