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Shortcut:
If a pipe can fill a tank in y hours and another pipe can empty the full tank in z hours, then the net part filled in 1 hour, when both the pipes are opened is
1
/
y
−
1
/
z
.
Therefore, Time taken to fill the tank, when both the pipes are opened =
yz
/
z − y
Here, y = 30, z = ?, Time = 40
Using these values in the shortcut, we get:
Required time =
30 x z
/
z − 30
40 =
30 x z
/
z − 30
40 x (z − 30) = 30z
40z − 1200 = 30z
40z − 30z = 1200
10z = 1200
z =
1200
/
10
= 120 minutes or 2 hours
Now, from the question, applying the rule we have, time taken by B to fill the tank when crack in the bottom develops =
120 x 40
/
120 − 40
= 60 minutes = 1 hour

