Question

..Two taps can fill a tank in 45 min-
utes and 60 minutes. Another
tap can empty it in 30 minutes.
If the tank is empty and all the 3
taps are kept open in how much
time the tank will be filled​

Answer 1

Answer:

Step-by-step explanation:

To Find,

Two taps can fill a tank in 45 min-utes and 60 minutes.

Another  tap can empty it in 30 minutes.

To Find,

Time taken to fill the tank.

Solution,

Let the three taps be Tap A, Tap B, and Tap C respectively.

Area filled by Tap A in 1 min = 1/45

Area filled by Tap B in 1 min = 1/60

Area emptied by Tap B in 1 min = 1/30

Total area filled by the taps A,B and C in one min = Tap (A + B) - Tap C

= (1/45 + 1/60) - 1/30

= (8 + 6 - 12)/360   [LCM of 45, 60 and 30 is 360)

= 2/360

= 1/180

Hence, taps will take 180 min to fill the tank.

Answer 2

Given :-

Two taps can fill a tank in 45 minutes and 60 minutes. Another  tap can empty it in 30 minutes.  If the tank is empty and all the 3  taps are kept open

To Find :-

Time taken

Solution :-

At first

Tap A can fill = 1/45 part in 1 min

Tap B can fill = 1/60 part in 1 min

Tap C can fill = 1/30 part in 1 min

Now,

We will found the sum of time taken by tap A and tap B

$\sf\dfrac{1}{45} + \dfrac{1}{60}$

$\sf \dfrac{4 + 3}{180}$

$\sf\dfrac{7}{180}$

Time taken = Time taken by A and B - Time taken by C

$\sf\dfrac{7}{180} - \dfrac{1}{30}$

$\sf\dfrac{7-6}{180}$

$\sf\dfrac{1}{180}$