Question

PipeA can fill a tank in 5 hours and pipe B in 10 hours both the pipes are opened together and after 2 hours pipe A is closed how much time will be taken by pipe B to fill the remaining tank?

Answer 1

part filled by pipe A in 1 hr = 1/ 5 litres

part filled by pipe B in 1 hr = 1/ 10 litres

since, pipe A and pipe B were opened together for 2 hours . then,

part A and B filled together:
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part filled in 2 hrs = 2 [ ( 1/ 5 )+ ( 1 /10 ) ]

= 2 × ( 15 /50 ) = 30 / 50 = 3 / 5 litre

remaining part = 1 - ( 3/ 5 ) = 2/ 5 litre

part filled by pipe B in 1 hr = 1 / 10 litre

let the time taken by pipe B to fill the remaining tank be ' x hr '

1/10 : 2/5 : : 1 : x

x / 10= 2/ 5 => x = 4hrs

therefore ,

the remaining part of tank will be filled by pipe B in 4hrs .

Answer : required time = 4 hours

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Answer 2

Pipe A can fill the tank in 5 hours

⇒ 1 hour = 1/5 of the tank

Pipe B can fill the tank in 10 hours

⇒ 1 hour = 1/10 of the tank

Find the amount of tank filled in 2 hours:

1 hour = 1/5 + 1/10 = 3/10 of the tank

2 hours = 3/10 x 2 = 6/10 = 3/5

Find the amount of water needed to fill:

Amount of water = 1 - 3/5 = 2/5 = 4/10 of the tank

Find the amount of time needed for pipe B to fill the rest of the tank:

1/10 of the tank = 1 hour

4/10 of the tank = 1 x 4 = 4 hours

Answer: Pipe B needs 4 hours to fill the remaining of the tank.