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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