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Two taps P and Q can fill a tank in 24 hours and 18 hours respectively. If the two taps are opened at 11 a.m., then at what time (in p.m.) should the tap P be closed to completely fill the tank at exactly 2 a.m?
- A5
- B2
- C3
- D4
Answer not set
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CCommunity
Let the capacity of the tank = 72 litres
Efficiency of pipe P = 72/24 = 3 litres/hour
Efficiency of pipe Q = 72/18 = 4 litres/hour
According to the question,
Total time in which tank has filled = 15 hours
Let the pipe P was closed at after n hours
According to the question
⇒ 3 × (n) + 4 × 15 = 72
⇒ 3n + 60 = 72
⇒ 3n = 12
⇒ n = 4
So, 4 hours after 11:00 am. that means 3:00 pm
∴ the tap P should be closed at 3 : 00 pm
Efficiency of pipe P = 72/24 = 3 litres/hour
Efficiency of pipe Q = 72/18 = 4 litres/hour
According to the question,
Total time in which tank has filled = 15 hours
Let the pipe P was closed at after n hours
According to the question
⇒ 3 × (n) + 4 × 15 = 72
⇒ 3n + 60 = 72
⇒ 3n = 12
⇒ n = 4
So, 4 hours after 11:00 am. that means 3:00 pm
∴ the tap P should be closed at 3 : 00 pm