Question

The ratio of efficiencies of two filling pipes is 4:5. There is a third emptying pipe which efficiency is two third of the average efficiency of
first two filling pipes can empty a filled tank in 36 minutes. Find how much time both the filling pipes can fill the tank when it is empty​

Answer 1

Given,

The ratio of efficiencies of two filling pipes is 4:5.

There is a third emptying pipe with efficiency of 2/3 of the average efficiency of  first two filling pipes.

The first two filling pipes can empty a filled tank in 36 minutes.

To find,

The time taken by both the filling pipes to fill the tank when it is empty​.

Let the efficiencies of filling pipes is 4a and 5a respectively (as ratio is 4:5).

Efficiency of pipe which empty the tank

= 2/3 x 9a/2 = 3a

Therefore, the total work

= 3a × 36 = 108a

Time to fill the tank by both the pipes

= 108a / 9a

= 12 min.

Therefore, 12 minutes is the time taken by both the filling pipes to fill the tank when it is empty​.

Answer 2

The time both the filling pipes can fill the tank when it is empty​ is 12 minutes.

Explanation:

The efficiency of the two filling pipes = 4 : 5

Let the efficiency of the two filling pipes be 4p and 5p respectively.

Efficiency of the empty pipe = 2/3 (4p + 5p)/2 = 2/3 × 9p/2 = 9p/3 = 3p

Now, the total work = 3p × 36 = 108p

Now, the time taken to fill both filling pipes is:

⇒ t = 108p/9p

∴ t = 12 minutes