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Bunuel
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A tank has two inlets: P and Q. P alone takes 6 hours and Q alone take 04 Feb 2021, 05:15
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35% (medium)

Question Stats:

73% (02:30) correct 27% (02:36) wrong based on 89 sessions

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A tank has two inlets: P and Q. P alone takes 6 hours and Q alone takes 8 hours to fill the empty tank completely when there is no leakage. A leakage was caused which would empty the full tank completely in ‘X’ hours when no inlet is open. Now, when only inlet P was opened, it took 15 hours to fill the empty tank completely. How much time will Q alone take to fill the empty tank completely ? (in hours)

(A) 40 hours
(B) 35 hours
(C) 26 hours
(D) 12 hours
(E) 10 hours
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A
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A tank has two inlets: P and Q. P alone takes 6 hours and Q alone take 07 Feb 2021, 11:53
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Leakage would empty 1/10 (1/6-1/15) of the tank per hour if no inlet is open. It would take Q to fill in 1/40 (1/8-1/10) of the pool in an hour with leakage. Therefore, it would take Q to fill in the whole tank in 40 hours.

Answer A.
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A tank has two inlets: P and Q. P alone takes 6 hours and Q alone take 07 Feb 2021, 23:26
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Ans A 40 hours

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A tank has two inlets: P and Q. P alone takes 6 hours and Q alone take 18 Feb 2021, 14:20
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Bunuel
A tank has two inlets: P and Q. P alone takes 6 hours and Q alone takes 8 hours to fill the empty tank completely when there is no leakage. A leakage was caused which would empty the full tank completely in ‘X’ hours when no inlet is open. Now, when only inlet P was opened, it took 15 hours to fill the empty tank completely. How much time will Q alone take to fill the empty tank completely ? (in hours)

(A) 40 hours
(B) 35 hours
(C) 26 hours
(D) 12 hours
(E) 10 hours
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Solution:

First, let’s determine the value of X. We see that the rates of inlets P and Q are 1/6 and 1/8, respectively. The rate of the leak is 1/X. Since it takes 15 hours to fill the empty tank completely when inlet P is filling and the leak is emptying, we can create the equation:

15(1/6 - 1/X) = 1

15/6 - 15/X = 1

Multiplying the equation by 6X, we have:

15x - 90 = 6X

9X = 90

X = 10

Now that we know X = 10, we can let N be the number of hours required to fill the empty tank completely when inlet Q is filling and the leak is emptying. We can create the equation:

N(1/8 - 1/10) = 1

N(1/40) = 1

N = 40

Answer: A
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