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Two taps P and Q can separately fill a tank in 120mins and 150 mins respectively. There is a 3rd tap in the bottom of the tank to empty it. If all of the 3 taps are simultaneously opened, then the tank is full in 100 mins. In how much time the 3rd pipe alone can empty the tank? A) 100 B) 200 C) 300 D) 400

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Two taps P and Q can separately fill a tank in 120mins and 150 mins respectively. There is a 3rd tap in the bottom of the tank to empty it. If all of the 3 taps are simultaneously opened, then the tank is full in 100 mins. In how much time the 3rd pipe alone can empty the tank? A) 100 B) 200 C) 300 D) 400
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B

Work done by the 3 tap in 1 min

= 1/100 – ( 1/120 + 1/150)

= 1/100 – (5+4/600)

=1/100 – 9/600

=6-9/600 = - 3/600

= - 1/200(negative signs mean empting)

Therefore the 3rd tap alone can empty the tank in 200 mins
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