Bissoy.com
Doctors Medicines MCQs Q&A

A and B can complete a task together in 35 days. If A works alone and completes 5/7 of the task and then leaves the rest for B to complete by herself, it will take a total of 90 days to complete the task. How many days would it take A, the more efficient among the duo, to complete the entire work by herself?

A and B can complete a task together in 35 days. If A works alone and completes 5/7 of the task and then leaves the rest for B to complete by herself, it will take a total of 90 days to complete the task. How many days would it take A, the more efficient among the duo, to complete the entire work by herself? Correct Answer 42

Let the total amount of work be 35 units.

If A and B work together, they complete 35/35 = 1 unit of work every day.

Now, let the amount of work done by A by herself in one day be x units and the work done by B by herself in one day be y units.

⇒ x + y = 1

If A works alone and completes 5/7th of the task, work done by A is (5/7) × 35 = 25 units.

⇒ time taken by A to complete this 25 units of work = 25/x days.

If B works alone and completes 2/7th of the task, work done by B is (2/7) × 35 = 10 units.

⇒ Time taken by B to complete this 10 units of work = 10/y days.

Total time taken is 90 days,

⇒ 25/x + 10/y = 90

⇒ 25y + 10x = 90xy

⇒ 25(1 – x) + 10x = 90xy

⇒ 25 – 25x + 10x = 90x(1 – x)

⇒ 25 – 15x = 90x – 90x2

⇒ 90x2 – 105x + 25 = 0

⇒ 18x2 – 21x + 5 = 0

⇒ 18x2 – 15x – 6x + 5 = 0

⇒ 3x(6x – 5) – 1(6x – 5) = 0

⇒ (6x – 5)(3x – 1) = 0

x = 5/6 (x cannot be 1/3 as A is more efficient among two)

∴ Time taken by A alone to complete work by herself = 35/ (5/6) = 42 days

Related Questions

A and B together can complete a task in 12 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A, how many days would it have taken B to do the work by herself?
A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken it have taken B to do the work by herself?
A and B together can complete a task in 12 days. However, if A works alone, completes half the job and leaves and then B works alone and competes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A, how many days would it have taken B to do the work by herself?
A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how many days would it have taken it have taken B to do the work by himself?
A and B together work for 3 days, B then worked alone for 2 days, A then worked alone for 3 days and the work was finished. If A works for 8 days alone and B works for 4 days alone, the work will be finished. How many days will A alone work if B works for 5 days alone?
Sharan and Mayukh, working together, can complete a task in 18 days. However, Mayukh works alone and leaves after completing one-third of the task. Then, Sharan takes over and completes the remaining work by himself. As a result, the duo could complete the task in 40 days. How many days would Sharan alone have taken to do the job if Mayukh had worked faster than Sharan?
If Arif works alone he will take 20 more hours to complete a task than if he works with Babu to complete the task. If Babu work alone, he will take 5 more hours to complete the task than if he works with Arif to complete the task. What is the ratio of the time taken by Arif to than taken by Babu if each of them works alone to complete the task?
X stars a certain work and after he completes exactly half the work, he leaves and Y takes up the remaining work and it takes a total of 45 days for the work to be completed this way. If X and Y working together can complete the work in 20 days, and Y is slower than X. Then, find the number of days in which the work will be completed, if X alone first works on exactly one-third, after which Y alone completes the rest of the work?
A and B together can do a piece of work in 60 days. B and C together can do the work in 40 days. A starts the work and works on it for 16 days then leaves. Then B takes up, works for 28 days, and leaves. Finally, C finishes the remaining work in 38 days. In how many days can B complete the entire work alone? 
Mugdha and Mayuri, working together, can complete a job in 18 days. However, Mayuri works alone and leaves after completing two-fifths of the job and then Mugdha takes over and completes the remaining work by herself. As a result, the duo could complete the job in 39 days. How many days would Mugdha alone have taken to do the job if Mayuri worked faster than Mugdha?