A works for 6 hours a day and B also works for 6 hours a day. What wil

Question

A works for 6 hours a day and B also works for 6 hours a day. What will be the number of days required to complete the work if only one of A and B work on any given day?

Statement 1: A and B working together for 6 hours everyday can complete the work in 4 days. 
Statement 2: A and B work 6 hours per day on alternate days to complete the work.

Source: Indian B-school entrance exam

chetan2u · Answer

Since, both work for 6 hours per day. But we do not know the speed of each nor who works for how many days.

Statement 1: A and B working together for 6 hours everyday can complete the work in 4 days. 
It is easy to fall in trap by taking 6 hrs per day work by each to be same speed. But it may be A finishes 20% in 6 hrs while B finishes 50% in 6 hrs. 
If both had same speed, then we could say that whatever be the speed , both will complete the work in 4*2 days. 
We just know 1/A+1/B=4
Insufficient

Statement 2: A and B work 6 hours per day on alternate days to complete the work.
We now know that both work for almost the same number of days unless the work gets over on an odd day. 
Example 5th day => A,B,A,B,A
Insufficient

Combined
We know they work on alternate days 
If they complete the work together in 4days, one day work of both combined is 1/4.
Working together on one day is same as one working on 1st day and second working on 2nd day. Thus they complete 1/4 work in two days ( working alternately), so total days required = 2/(1/4)=8 days

C

Mahima1203 · Answer

Won't combining 1&2 mean - A and B working together for 6 hours per day on alternate days can complete the work in 4 days?
Also, will you be able to explain it algebraically (through equations created for Statement 1 and for Statement 2 and then combine them)?

abhishekmayank · Answer

Hi  Bunuel ,

Could you help in solving the problem.

If amount of work done by A in 6 Hrs = A and amount of work done by B in 6 Hrs = B then

Total work done in 6 hours in 1 day if A and B are working together = A+B

Since both completes the work in 4 days, working together all 4 days and 6 Hrs each, the amount of work involved = 4(A+B)

If the same amount of work is done on alternate days by A and B alone, number of days to complete 4(A+B) work should be 8 days.

Where I am getting wrong ?

sujoykrdatta · Answer

S1. Not sufficient since the rates of doing work by A and B isn't given.

S2. Not sufficient since we don't know how many days the work lasted.

Combining: we have the following:

(A = work of A in 6 hrs and B = work of B in 6 hrs)

-   -   -   
Day1 - Day2 - Day3 - Day4

If it is done by A and B alternatively, we get:

-{B}- -{B}- -{B}- -{B}
D1 -D2 -D3 -D4 -D5 -D6 -D7 -D8

Thus, it takes 8 days - Sufficient

Answer C

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A works for 6 hours a day and B also works for 6 hours a day. What wil

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