Question

Three taps A, B and C can fill a tank in 10 minutes, 15 minutes and 20 minutes respectively. If the taps were shut off after 5 minutes, what is the volume of water that overflowed in %?​

Answer 1

Given data :

• Three taps A, B and C can fill a tank in 10 minutes, 15 minutes and 20 minutes respectively.

• The taps were shut off after 5 minutes.

To find :

The volume of water that overflowed in %, if the taps were shut off immediately after 5 minutes.

Calculation :

Tap A can fill the tank in 10 minutes. So, work done per minute = $\frac{1}{10}$ units

Tap B can fill the tank in 15 minutes. So, work done per minute = $\frac{1}{15}$ units

Tap C can fill the tank in 20 minutes. So, work done per minute = $\frac{1}{20}$ units

Total work done by them together = $\frac{1}{10} + \frac{1}{15} + \frac{1}{20}$ units

LCM of 10, 15, 20 is 60.

                                                           = $\frac{6+4+3}{60}$

                                                           = $\frac{13}{60}$

Total work done combinedly to fill the tank completely  = $\frac{13}{60}$ units

Total time taken to completely fill the tank = $\frac{60}{13}$  = 4.61538461538 minutes

So, it takes 4.61538461538 minutes to fill the tank of 60 units work i.e., 100% of the tank, combinedly.

The time overflow happenend =

Time at which taps shut off - time taken by taps to fill the tank completely

                                                  = 5 - 4.61538461538

                                                 = 0.38461538461 minutes

So, If 4.61538461538   =    100%

         0.38461538461  =     ? %

The volume of water overflowed =  $\frac{0.38461538461 * 100}{4.61538461538}$  

                                                       =  38.461538461 / 4.61538461538

                                                       =  8.33333333334 %

Therefore, the volume of water overflowed is  8.33% approximately.

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