tap A can fill a tank in 7 hrs. while tap B can empty the fill tank in 17/2 hrs. tf both the taps are opened together, how much time will they take to fill the tank completely?
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Let us name the 3 Taps be T
A
,T
B
,T
C
where T
B
,T
C
are emptying pipes and T
A
is filling Pipe.
Water Emptied by T
B
in 6 hours=Volume of Tank or V
Water Emptied by T
B
in 1 Hour=
6
V
Similarly, Water Emptied by T
C
in 8 Hour=V
Water Emptied by T
C
in 1 Hour=
8
V
Similarly, Water Supplied by T
A
in 2 Hour=V
Water Supplied by T
A
in 1 Hour=
2
V
After 2 Hours,
⇒2
2
V
−2
8
V
−2
6
V
=
12
5V
After 3 Hours,
⇒
12
5V
+
2
V
−
6
V
=
4
3V
Now, only T
A
is opened
Remaining Volume=V−
4
3V
=
4
V
Now Time taken to Fill Remaining Tank
⇒
2
V
4
V
=
2
1
hrs=30min
Therefore Answer is (C)
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