Question
There are two inlets A and B connected to a tank. A and
B can fill the tank in 16 h and 10 h, respectively. If both the pipes are opened alternately for 1 h, starting with A, then in how much time (in hours, to nearest integer) will the tank be filled?Solution
ATQ, we can say that Pipe A can fill the tank in 16 hour Part of the tank filled by pipe A in 1 hour = 1/16 Pipe B can fill a tank in 10 hours Part of the tank filled by B in 1 hour = 1/10 The part filled by (A + B) in 2 hours = [(1/16) + (1/10)] (5 + 8)/80 13/80 Now, 6 × (13/80) = 78/80 In 6 × 2 = 12 hours tank filled by 78/80 part Remaining is (1 - 78/80) part 2/80 = 1/40 part After complete of 12 hours pipe A will be open To fill 1/16 part pipe A takes time 1 hour To fill 1/40 part pipe A will take time (16/40) hour (2/5) hour 24 minutes [∵ 1 hour = 60 min] Total time needed to fill the tank (12 hours + 24 minutes) 12 hours 24 minutes ∴ Starting from A 12 hours 24 minutes will take to fill the tank.
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