Question

Two pipes a and b can fill a tank in 12 min and 16 min respectively. If both the pipes are opened together, then after how much time , b should be closed so that the tank is full in 9 min

Answer 1

Part of the cistern filled by pipe P in 1 min =
1
12

Part of the cistern filled by pipe Q in 1 min =
1
16


Suppose Q should be closed after
x
minutes

i.e., Pipe P and Q will be open for initial
x
minutes then P will be open for another (9-x) min
x
(
1
12
+
1
16
)
+
(
9
−
x
)
1
12
=
1
7
x
48
+
9
12
−
x
12
=
1
7
x
+
36
−
4
x
=
48
3
x
=
12
x
=
4