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

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

Answer:

Quantity of water filled by the first tap in one minute =301

Quantity of water filled by the second tap in one minute =401

Quantity of water emptied by the third tap in one minute =241

Quantity of water filled in one minute, when all the 3 taps are opened =301+401−241

                                                                                                      =1204+3−5=1207−5

                                                                                                      =1202=601

Time taken to fill the tank =6011=60 minutes

                                        =1 hour