1.

1). 1 hr. 3 min.2). 1 hr. 18 min.3). 1 hr. 24 min.4). 1 hr. 42 min.

Answer»

Part filled by PIPES A & B in 1 hr = 1/4

Part emptied by pipe C in 1 hr = 1/10

Part emptied by pipe D in 1 hr = 1/12

Now, pipe A & B were open for = 3 hours

Pipe C was open for = 3 - 1 = 2 hours

Let pipe D was opened after ‘X’ hours of opening of pipe C,

Pipe D was open for = (2 - x) hours

Hence, part filled in 3 hours = 1/2

⇒ Part filled by A & B - Part emptied by C & D = 1/2

⇒ 3 × (1/4) - 2 × (1/10) - (2 - x) × (1/12) = 1/2

⇒ 3/4 - 1/5 - (2 - x)/12 = 1/2

⇒ 45 - 12 - 10 + 5x = 30

⇒ 5x = 7

⇒ x = 7/5 = 1.4 HRS = 1 hr. 24 min.

∴ Pipe D was opened after 1 hr. 24 min. of opening of pipe C



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