Question

pipe A can fill a cistern in 4 hours while pipe B can empty it in 6 hours .if both ofbthem are opened at same time when the cistern is empty ,the number of hours taken by them to fill is​

Answer 1

Solution :

Pipe A can fill a cistern in 4 hours

So, the portion of work done by pipe A in 1 hour = 1/4

Pipe B can empty a cistern in 6 hours

So, the portion of work done by pipe B in 1 hour = - 1/6 [ - indicates empty ]

We know that

Portion of work done by both Pipe A and pipe B = Portion of work done by Pipe A + Portion of work done by Pipe B

= 1/4 + [ - 1/6 ]

= 1/4 - 1/6

Taking LCM

= (3 - 2)/12

= 1/12

= 1/12

i.e Portion of work done by both Pipe A and pipe B = 1/12

⇒ Pipe A and pipe B together can fill in = 12 hours

Hence, the number of hours taken by them to fill is 12 hours.

Answer 2

Given :---

• pipe A can fill a cistern in = 4 hours
• pipe B can empty it in = 6 hours

Solution :----

LCM of 6 and 4 = 12litre = let capacity of cistern.

Efficiency of A = 12/4 = 3 litre/hour

Effeciency of B = 12/6 = (-2) litre/hour (since it is a outlet pipe)

so, effeciency of both per hour = 3+(-2) = 1 litre /hour .

Numbers of hours taken by both of them to Fill the tank now, = 12/1 = 12 hours (Ans)

so, both A and B , when opened together they can fill the cistern in 12 hours ..

(Hope it Helps you)