2 pipes A & B can fill a cistern in 12 min and 16 min resp. If both pipes are opend together then after hw mch time B shld be closed so tht the...

A  alone can fill  1/12 of the cistern in 1
minute.

B alone can fill (1/16)th of the
cistern.

Let the  pipes work together for x minutes to fill
the empty cistern

So in x minutes (1/12+1/16)x =  7x/48 of
the cistern is filled up.

If B is closed at the xth minute,
then the rest of the tank to be filled up by A alone = 1- 7x/48 =
(48-7x)/48.

(49-7x)/48 of the cistern can be filled by A in
{(48-7x)/48}/(1/12) minutes

Therefore  x+
{(48-7x)/48}/(1/12) = 9 minutes

=> x+(48-7x)/4 =
9

=>4x +(48-7x) =
9*4

=> 4x+48-7x =
36

=> 48-36 =
7x-4x

=> 12 =
3x

=> x = 12/3 hrs = 4
mins.

Therefore, B should be closed after 4
minutes so that the pipe A can fill the cistern is full in the 9
minutes.