arithmetic - two pipes a and b can fill a cistern in 12 minutes and 16 minutes 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 minutes - skillgun

Let B be closed after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (9 — x) min, = 1
x[(1/12) + (1/16)] + (9 - x)(1/12) = 1 or (7x/48) + (9-x)/12 = 1
or 7x + 36 - 4x = 48 or x=4.
So, B must be closed after 4 minutes.