Question : An inlet pipe can fill an empty tank in 140 hours, while an outlet pipe drains a filled tank in 63 hours. If 8 inlet pipes and y outlet pipes are opened simultaneously, when the tank is empty, then the tank gets filled in 105 hours. Find the value of y.
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3
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Correct Answer: 3
Solution : Inlet pipe can fill in = 140 hours Outlet pipe can drain in = 63 hours LCM of 140 and 63 is 1260 Total work = 1260 units Efficiency of inlet pipe = $\frac{1260}{140}$ = 9 units/hours Efficiency of outlet pipe = $\frac{1260}{63}$ = 20 units/hours Given: Number of outlet pipes = y We know that, Work = Efficiency × Time According to the question, 1260 = (9 × 8 – 20y) × 105 ⇒ 1260 = (72 – 20y) × 105 ⇒ 1260 – 7560 = – 2100y ⇒ 6300 = 2100y ⇒ y = 3 Hence, the correct answer is 3.
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