PIPES AND CISTERNS

Daniel sir ,
i have a doubt in pipes and cisterns topic like if already the tank is filled some volume...
see i'am writing the question below...

Q):A water tank is two-fifth full. pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?
a)6min. to empty
b)6min. to fill
c)9min. to empty
d)9min. to fill

Ok so this is how you solve it

If pipe A fills the tank in 10 mins, means every minute it fills (1/10)th of the tank
If pipe B empties the tank in 6 mins, means every minute it empties (1/6)th of the tank

So if both the pipes are on, the net work done every minute is (1/10) - (1/6) = (6-10)/60 = -4/60 = -1/15

So now -1/15 is getting emptied every min that the two pipes are open


Consider this : Your tank is 2/5 full   Since its a fraction, we can multiply the same number in the numerator and denominator without changing the value right ?

Multiply 3 on top and below
So (2 X 3)/(5 X 3) = 6/15

So now since the part of the tank with water is 6/15 and the net work of pipes A & B is -1/15 ......

The pipes will empty the tank in 6 mins

Hence the correct answer is (a) 6 min to empty

Is your Doubt cleared ?  

thanks