Question
Two pipes, A and B, can fill a tank in 10 minutes and 20
minutes, respectively. The pipe C can empty the tank in 30 minutes. All the three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. In what time, will the tank be full (in minutes)?Solution
A fills in 10 min: 1/10 per min B fills in 20 min: 1/20 per min C empties in 30 min: − 1/30 per min Let the time taken to fill the tank is x minutes. When all 3 are opened = 1/10+ 1/20 – 1/30 = 7/60 per min Volume filled by all three pipes in (x – 2) minutes = (7/60) X (x - 2) Volume filled by A and B alone in the last 2 minutes = 1/10 + 1/20 = 3/20 Volume filled = 3/20 x 2 = 3/10 Now, (7/60) X (x - 2) + 3/10 = 1 Or, (7/60) X (x - 2) = 1 – (3/10) Or, (7/60) X (x - 2) = (7/10) Now, x = 8
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