Two pipes A and B can fill in 40 minutes and 30 minutes respectively.Both the pipes are open together but after 5 minutes, pipe B is turned off.What is the total time required to fill the tank?

we see that both pipes together can fill the the tank in 120/7 minutes:

1/t = 1/40 + 1/30
t = 7/120

So, after 5 minutes, they have filled 35/120 = 7/24 of the tank.

So, it will take A 7/24*40 = 35/3 minutes to fill the rest.

Total time: 5 + 35/3 = 16 2/3 minutes.

T = Ta*Tb/(Ta+Tb) = 40*30/(40+30)= 17.14 Min. to fill with both pipes open.

(17.14-5)/17.14 = 0.708 of a tank
to be filled.

5 + 0.708*40 = 33.34 Min., total.

To find the total time required to fill the tank, we need to calculate the amount of work done by both pipes A and B.

Let's assume that the tank has a capacity of 1 unit.

In 1 minute, pipe A can fill 1/40 of the tank's capacity
In 1 minute, pipe B can fill 1/30 of the tank's capacity

When both pipes A and B are open for 5 minutes, the work done by pipe A is (1/40) * 5 = 1/8
After 5 minutes, only pipe A is working and pipe B is turned off, so pipe A will continue filling the tank.

Now, let's calculate the time required for pipe A to fill the remaining 7/8 of the tank's capacity.
Pipe A can fill 1/40 of the tank's capacity in 1 minute.
Therefore, it will take pipe A (7/8) * 40 = 35 minutes to fill the remaining part of the tank.

So, the total time required to fill the tank is 5 minutes (when both pipes A and B are open) plus 35 minutes (when only pipe A is working after turning off pipe B), which equals 40 minutes.