Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes

Correct Option: B

Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes
∴ In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled
∴ Requied answer = 1 - 5/24 = 19/24 part

Let the first pipe be shut up after x minutes
Now, applying the given rule, we have 30{1 - (x + 10)/40 } = x

Correct Option: B

Let the first pipe be shut up after x minutes
Now, applying the given rule, we have 30{1 - (x + 10)/40 } = x
[Here t = (x + 10) minutes]
or x = 90/7 minutes

Here w = 2 litres per hour
∴ Required answer = {(15 x 10) / (15 - 10)} x 2 = 60 litres.

Correct Option: B

Here w = 2 litres per hour
∴ Required answer = {(15 x 10) / (15 - 10)} x 2 = 60 litres.

Part filled by tap A in 1 min = 1/60
Let tap B fills the tank in x min
Then, Part filled by tap, B in 1 min = 1/x
According to the question,
1/60 + 1/x = 1/40

Correct Option: D

Part filled by tap A in 1 min = 1/60
Let tap B fills the tank in x min
Then, Part filled by tap, B in 1 min = 1/x
According to the question,
1/60 + 1/x = 1/40
⇒ 1/x = 1/40 - 1/60
&rArr ; 1/x = (3 - 2)/120
&rArr ; 1/x = 1/120
∴ Tap B can fill the tank in 120 min.

Part of tank filled by first tap in 1 h = 1/3
Part of tank filled by second tap in 1 h = 1/4
Part of tank emptied by third tap in 1 h = 1/5
Part of the tank filled by all pipes opened simultaneously in 1 h
= 1/3 + 1/4 - 1/5 = (20 + 15 - 12)/60 = 23/60

Correct Option: B

Part of tank filled by first tap in 1 h = 1/3
Part of tank filled by second tap in 1 h = 1/4
Part of tank emptied by third tap in 1 h = 1/5
Part of the tank filled by all pipes opened simultaneously in 1 h
= 1/3 + 1/4 - 1/5 = (20 + 15 - 12)/60 = 23/60
Time taken by all the taps to fill the tank when it is empty = 23/60 h = 2¹⁴/₂₃ h