Question : Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
Option 1: 4:40 p.m.
Option 2: 5:40 p.m.
Option 3: 6:20 p.m.
Option 4: 7:20 p.m.
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Correct Answer: 5:40 p.m.
Solution : LCM of 20, 30 and 60 is 60. Let, the capacity of the tank = 60 units Efficiency of A = $\frac{60}{20} = 3$ Efficiency of B = $\frac{60}{30} = 2$ Efficiency of C = $\frac{60}{60} = 1$ Let the time taken by pipes to fill the tank be $x$ hours. According to the question, Let A work for $x$ hours B works for $(x - 1)$ hours C works for $(x - 2)$ hours We know that total work = efficiency × time So, $60 = 3x + 2 (x - 1) + 1 (x - 2)$ ⇒ $60 = 6x - 4$ ⇒ $6x = 64$ ⇒ $x = \frac{32}{3} = 10\frac{2}{3}=$ 10 hrs 40 min Since A starts at 7 a.m Tank will fill at 7 a.m + 10 hrs 40 min = 5:40 p.m Hence, the correct answer is 5:40 p.m.
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