let's assume the task is to place bricks and 24 (common to both, 8 and 24) bricks need to be placed.

so alan takes 8 hours to place 24 bricks
in one hour, he places 3 bricks (cross multiplication)

now bob takes 12 hours to place 24 bricks
so in 1 hour, he places 2 bricks.

alan works for 4 hours. 3*4 = 12 bricks
now bob joins him. so from now on, together they place 3 + 2 = 5 bricks in one hour

12 are placed, 12 more to go. 12/5 = 2.4 hours.

so the first 4 hours + 2.4 hours = 6.4 hours. hence, D

But the question asks for how many hours will Allan have worked by the time the task is finished.
So why are we adding the time spent by Bob also ?

bhumika.k.shah wrote:Allan can complete the task in 8 hours. Bob can complete the task in 12 hours. If Allan works on the task alone for 4 hours and then Bob starts to help him, how many hours in total will Allan have worked by the time the task is finished?

A.5
B.5.2
C.5.6
D.6.4
E.7.2

OA D

i dint quite understand what is really needed

the question posted by you asks about Alan, not Bob.

bhumika.k.shah wrote:Allan can complete the task in 8 hours. Bob can complete the task in 12 hours. If Allan works on the task alone for 4 hours and then Bob starts to help him, how many hours in total will Allan have worked by the time the task is finished?

A.5
B.5.2
C.5.6
D.6.4
E.7.2

Picking numbers is one great approach - we can also solve using the work formula, as long as we're careful.

If it takes Allan 8 hours to do a full job, then in 4 hours he'll have completed exactly 1/2 the task.

To complete 1/2 the job, it takes Allan 4 hours and Bob 6 hours (1/2 of the 12 hours it takes to do the full job). Now we can use the simple work formula:

Combined time (2 workers) = A*B/(A+B)

in which A and B are the times it takes them to do the job alone.

So:

CT (Allan and Bob) = 4*6/4+6 = 24/10 = 2.4 hours.

So, Allan worked 4 hours alone and then 2.4 hours in conjunction with Bob for a total of 6.4 hours: choose (D).