arithmetic - two pipes p and q can fill a tank in 12 min and 16 min respectively if both the pipes are opened simultaneously after how much time q should be closed so that the tank is full in 6 minutes - skillgun

Solution: Let Q be closed after x minutes. Then,
Part filled by (P+Q) in x min. + part filled by P in (6 -x) min. = 1.
.'. x(1/12 + 1/16) + (6 - x)*1/12 = 1
=> 7x/48 + (6- x)/12 = 1.
=> 7x + 4(6-x) = 48
=> 3x = 48 - 24
=> x = 24/3 = 8.
Hence, Q must be closed after 8 minutes.