Question

Pipes A and B can fill an empty tank in 40 minutes and 60 minutes, respectively and pipe C alone can
empty full tank in x minutes. All the three pipes are opened for 24 minutes and then C is closed. A and B
together fill the tank in another 16 minutes. What is the value of x ?​

Answer 1

Answer:

36 minutes

Step-by-step explanation:

A can fill the tank in 1/40

B can fill the tank in 1/60

C can empty the tank in 1/x

Both A and B can fill the tank in 1/40 +1/60 =1/24

All the 3 pipes can fill the tank in 1/24-1/x

As all the 3 pipes are opened for 24 min and C is closed. A and B fill the tank in another 16 min. So,

[24*(1/24-1/x)+16*(1/24)] = 1 (since, time to fill a single tank)

solving the above eq,

we get  x=36 min

Answer 2

Given:

Time taken by pipe A = 40 min

Time taken by pipe B = 60 min

Time taken by C to empty the tank = x min

Total time of opening = 24 mins

A and B fill tanks in = 16 mins

To Find:

Value of x

Solution:

Time taken by A to fill the tank = 1/40

Time taken by B to fill the tank = 1/60

Time taken by C to empty the tank = 1/x

Time taken A and B can fill the tank -

= 1/40 +1/60

=1/24

All the 3 pipes can fill the tank in -

=  1/24 - 1/x ( as C empties it in x mins)

Now, A and B also fill the tank in another 16 min.

Thus,

= 24 x (1/24-1/x) + 16 x (1/24) = 1 (since, time to fill a single tank)

= 24 x ( x - 24/24x ) + 2/3= 1

= 24x - 576/24x = 1/3

= 3( 24x - 576) = 24x

= 72x - 1728 = 24x

x = 36

Answer: C will empty the tank is 36 minutes.