Part filled by A in 1 hr= (1/45)
Part filled by B in 1 hr= (1/36)

Correct Option: C

Part filled A in 1 hr= (1/45)
Part filled B in 1 hr= (1/36)
Part filled by (A+B) together in 1 hr=(1/45)+(1/36)=1/20

So, The tank will be full in 20 hr.

We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m

Correct Option: B

We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m
Here, m = 6
∴ Required part of the tank to be filled in 1 h = 1/6 part

Let the leak empties the full tank in x h, then
Part emptied in 1 by leak = 1/x
Part filled by inlet in 1 h = 1/20
According to the question,
1/20 + 1/x = 1/40

Correct Option: A

Let the leak empties the full tank in x h, then
Part emptied in 1 by leak = 1/x
Part filled by inlet in 1 h = 1/20
According to the question,
1/20 + 1/x = 1/40
∴ 1/x = 1/40 - 1/20 = 1- 2/40 = -1/40 [-ve sign Indicates emptying.]
Clearly, leak will empty the full tank in 40 h.

Time taken by the pipe to empty the cistern = 3 h
Then, time taken by the pipe to empty the 2/3 part = 3 x 2/3 = 2 h

Correct Option: B

Time taken by the pipe to empty the cistern = 3 h
Then, time taken by the pipe to empty the 2/3 part = 3 x 2/3 = 2 h

When a pipe fills 1/m part of a tank in 1 h, then the pipe takes m h to fill the tank.

Correct Option: D

We know that, when a pipe fills 1/m part of a tank in 1 h, then the pipe takes m h to fill the tank.
Here, 1/m = 1/8 ⇒ m = 8
∴ Required time to fill the tank = 8 h