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17 Jan 2022, 03:15
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D
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Difficulty:
95%
(hard)
Question Stats:
53% (03:16) correct
47%
(03:17)
wrong
based on 129
sessions
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A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
I. 32
II. 54
III. 29
IV. 40
A. I and II only
B. I and III only
C. II and IV only
D. II and III only
E. I and IV only
Are You Up For the Challenge: 700 Level Questions
I. 32
II. 54
III. 29
IV. 40
A. I and II only
B. I and III only
C. II and IV only
D. II and III only
E. I and IV only
Are You Up For the Challenge: 700 Level Questions
17 Jan 2022, 04:04
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[quote="Bunuel"]A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
I. 32
II. 54
III. 29
IV. 40
A. I and II only
B. I and III only
C. II and IV only
D. II and III only
E. I and IV only
Let, x pipes fill, then n-x must drain.
\(\frac{x}{20}\) - \(\frac{(n-x)}{30}\) =\(\frac{1}{5}\)
5x-2n = 12
x = \(\frac{2*(6+n)}{5}\)
For x to be an integer, (6+n) must be divisible by 5.
54 & 29 satisfies this.
So, D (IMO)
I. 32
II. 54
III. 29
IV. 40
A. I and II only
B. I and III only
C. II and IV only
D. II and III only
E. I and IV only
Let, x pipes fill, then n-x must drain.
\(\frac{x}{20}\) - \(\frac{(n-x)}{30}\) =\(\frac{1}{5}\)
5x-2n = 12
x = \(\frac{2*(6+n)}{5}\)
For x to be an integer, (6+n) must be divisible by 5.
54 & 29 satisfies this.
So, D (IMO)
General Discussion
11 Apr 2025, 00:16
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Bunuel
Let the number of fill pipes be “a”
Let the number of drain pipes be (n-a)
Total number of pipes ( fill and drain) is n
LCM (20,30) = 60 , which is the capacity of the tank.
Fill pipe takes 20 hrs to fill, hence efficiency = 60/20 = 3
Drain pipe drains the tank in 30 hrs, efficiency = 60/30 = -2 (-ve since drain)
It’s mentioned in 5 hrs of fill and drain pipe working together fills the tank of capacity 60 units.
5 * [3a - 2(n-a) ] = 60
3a - 2n +2a =12
5a -12 = 2n
Substitute the values of n from the options
I. 32
5a -12 = 64 , not divisible by 5 . Hence, eliminated.
II. 54
5a -12 = 2*54
5a -12=108
5a = 120,
hence a = 24. Integer value.
III. 29
5a -12 = 2*29
5a -12 = 58
a = 16 is an integer.
IV. 40
5a -12 = 2*40
5a = 92
not an ineger.
Option D (II AND III)
