Question

An empty cisteen can be filled by two pipes A and B in 12 minutes and 16 minutes respectively and be emptied by a third pipe C in 8 minutes. If all the pipes are turned on at the same time, in how much time will the cistern take to be full?​

Answer 1

Step-by-step explanation:

let's take the work constant

i.e LCM( 12,16,8)=96units

A does 96/12 = 8u/min

B does 96/16= 6u/min

C does 96/8 = 12u/min ( which is negative work)

all together do (8+6-12)=2u/min

To do 96units they take 48minutes

Answer 2

A fills in 1 min=1/12 of the cistern,

B fills in 1 min=1/16 of the cistern,

C empties in 1 min=1/8 of the cistern,

Together they fill (1/12+1/16-1/8) --------------->4+3-6/48

Together they fill 1/48 of the cistern is 1 min

Time taken by A, B and C together = 48 mins.