8 taps are fitted in a tank, some are water taps and rest are outlet taps. Each water tap can fill the tank in 12 hrs and each outlet tap can empty it in 36 hrs. Find the number of outlet water taps, if the whole tank can be filled in 3 hrs.
Answers
Given : 8 taps are fitted in a tank, some are water taps and rest are outlet taps. Each water tap can fill the tank in 12 hrs and each outlet tap can empty it in 36 hrs.
To Find : the number of outlet water taps, if the whole tank can be filled in 3 hrs.
Solution:
Each water tap can fill the tank in 12 hrs
=> Each water tap can fill the tank in 1 hr = 1/12
Each outlet tap can empty it in 36 hrs
=> Each outlet tap can empty in 1 hr = 1/36
Let say water tap = W
& outlet Tap = 8 - W
W water tap can fill the tank in 1 hr = W/12
W water tap can fill the tank in 3 hr = 3 * W/12 = W/4
8 - W outlet tap can empty in 1 hr = (8 - W) /36
8 - W outlet tap can empty in 3 hr = 3 *(8 - W) /36 = (8 - W )/12
W/4 - (8 - W )/12 = 1
=> 3W - (8 - W) = 12
=> 4W = 20
=> W = 5
Water Taps = 5
Outlet Tap = 3
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