Question

Two taps take 10 and 20 minutes to fill an empty cistern. But they take 25 minutes due to a leak. In how time will the tank be emptied by leak?

Answer 1

Answer:

The leak can empty the tank in 9.09 minutes

Step-by-step explanation:

tap A take 10 min to fill the tank

=> amount of tank filled in 1 minute by tap A = 1/10

tap B take 20 min to fill the tank

=> amount of tank filled in 1 minute by tap B = 1/20

let the leakage empty the tank in t minutes

=> amount of tank emptied in 1 minute by leak = 1/t

Hence all three together opened , the amount of tank filled in 1 minute

= 1/10  +  1/20  - 1/t

Given tank will be filled in 25 minutes

=> amount of tank filled in 1 minute = 1/25

hence,

1/10  +  1/20  - 1/t = 1/25

=> 1/t = 1/10  +  1/20  - 1/25

=> 1/t = (10 + 5 - 4)/100 = 11/100

=> t = 100/11 = 9.09 minutes

Hence the leak can empty the tank in 9.09 minutes

Answer 2

Answer:

100/11 minutes

Step-by-step explanation:

Hi,

Given that Tap 1 takes 10 minutes to fill an empty cistern

In 1 min, tap 1 fills 1/10 th of cistern

Given that Tap 2 takes 20 minutes to fill an empty cistern

In 1 min, tap 2 fills 1/20 th of cistern

Let the leak takes 'x' min to empty full cistern,

In 1 min, leak empties 1/x th of full cistern

If both the taps and leak are open together, then in 1 min,

1/10 + 1/20 - 1/x is filled

Given that it takes 25 minutes to fill, so in 1 min they should fill 1/25 th

So, 1/10 + 1/20 - 1/x = 1/25

1/x = 1/10 + 1/20 - 1/25

1/x = (10 + 5 - 4)/100

1/x = 11/100

x = 100/11 mins

Hence leak takes 100/11 mins to empty the full tanks.

Hope, it helps !