Taps A and B can fill a tank in 12 mins and 15 mins respectively. If both are opened and A is closed after 3 mins, how long will it take for B to fill the tank?
Answer
In 1 min the tap A fills ---------- 1/12 th part of the tank
in 1 min the tap B fills ------------1/15th part of the tank.
In 1 min the two taps can together fill -----(1/12) + (1/15) = 9/60
in 3 mins the two taps can together fill -----3 x 9/60 = 27/60
So, the tank left to be filled = 1 - 27/60 = 33/60
Now 33/60th part of the tank will be filled by B in = (33/60) / (1/15) = 33 x 15 / 60 = 33/4 mins
So, tap B will fill the remaining tank in 33/4 mins = 8 mins and 15 secs
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Answer
In 1 min the tap A fills ---------- 1/12 th part of the tank
in 1 min the tap B fills ------------1/15th part of the tank.
In 1 min the two taps can together fill -----(1/12) + (1/15) = 9/60
in 3 mins the two taps can together fill -----3 x 9/60 = 27/60
So, the tank left to be filled = 1 - 27/60 = 33/60
Now 33/60th part of the tank will be filled by B in = (33/60) / (1/15) = 33 x 15 / 60 = 33/4 mins
So, tap B will fill the remaining tank in 33/4 mins = 8 mins and 15 secs
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