Question

A and B together can build a wall in 30 days.if A is twice as good as a workman as B,in how many days will A alone finish the work?​

Answer 1

Let a be the working rate of A

Let b be the working rate of B

Since A is twice as good as B, this means that 2a = b — which means that you would need 2 B's to work at the same rate as A, or, two employees working at B's level is equal to 1 A.

A and B the working together to finish their work in 30 days.

Therefore,

30 = a + b

30 = a + 2a

30 = 3a

a = 10

This means, it took A 10 days to finish the project with B, and it took B

2a = b

=> 2(10) = b

=> b = 20

It took B 20 days to finish the work with A.

Now if A is doing the same amount of work alone, he needs to do B's 20 days of work.

Since 2a = b

=> 2a = 20

=> a = 10

This means, that A will complete his original 10 days of work, plus B's 20, which will take him 10 days to do.

Therefore, it will take him (10 + 10) = 20 days to do the work.

This is a linear solution to the problem, because it assumes that A works his full 10 days, and then stops, to let B do his fair share of work (basically, A and B split the work in 2, and they work separately)

Now realistically, what would or might happen instead, is A would likely continue working after finishing his half of the work, to make it easier for B.

Assuming this is the case instead, this implies that the time is split in half - so A does 15 days of work, and B does 15 days shift of work.

If A is now doing the work alone, he needs to complete B's 15 days, which, since 2a = b, will take him:

2a = b

2a = 15

a = 7.5

Therefore, it will take A his original 15 days, plus B's 15 days (= A's 7.5 days) to finish the work.

15 + 7.5 = 22.5

Therefore, it will take A 22.5 days to finish the job.

Step-by-step explanation:

Hope this answer will be helpful..