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07 Apr 2020, 09:29
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E
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Difficulty:
75%
(hard)
Question Stats:
64% (03:11) correct
36%
(03:43)
wrong
based on 166
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A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?
A. 40
B. 42
C. 44
D. 46
E. 48
Are You Up For the Challenge: 700 Level Questions
A. 40
B. 42
C. 44
D. 46
E. 48
Are You Up For the Challenge: 700 Level Questions
07 Apr 2020, 10:08
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Let x and y be the amount of water of each inlet brings into the water tank per minute via inlets of types of A and B, respectively.
\(30 (10x + 45y) =1 \)
\(60 (8x + 18y )= 1\)
--> \(10x + 45y = \frac{1}{30}\)
--> \(4x + 9y = \frac{1}{120}\)
Adding them together:
\(14x+ 54y = \frac{1}{30}+\frac{ 1}{120}= \frac{5}{120} = \frac{1}{24}\)
\(2 (7x + 27y) = \frac{1}{24}\)
--> \(48 (7x+ 27y) = 1\)
if 7 inlets of type A and 27 inlets of type B are open, \(48\) minutes will the empty tank to get fulfilled.
Answer (E).
\(30 (10x + 45y) =1 \)
\(60 (8x + 18y )= 1\)
--> \(10x + 45y = \frac{1}{30}\)
--> \(4x + 9y = \frac{1}{120}\)
Adding them together:
\(14x+ 54y = \frac{1}{30}+\frac{ 1}{120}= \frac{5}{120} = \frac{1}{24}\)
\(2 (7x + 27y) = \frac{1}{24}\)
--> \(48 (7x+ 27y) = 1\)
if 7 inlets of type A and 27 inlets of type B are open, \(48\) minutes will the empty tank to get fulfilled.
Answer (E).
General Discussion
07 Apr 2020, 17:06
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1=(10/a + 45/b)(1/2)
1=(8/a + 18/b)(1)
2 =10/a + 45/b
1 = 8/a + 18/b
4 =20/a + 90/b
5 = 40/a + 90/b
..
1 = 20/a --> a=20
..
2 = 10/20+45/b--> b=30
1 = (7/20+27/30)t
t=60/75
t=12/15
12/15*60 = 48min
1=(8/a + 18/b)(1)
2 =10/a + 45/b
1 = 8/a + 18/b
4 =20/a + 90/b
5 = 40/a + 90/b
..
1 = 20/a --> a=20
..
2 = 10/20+45/b--> b=30
1 = (7/20+27/30)t
t=60/75
t=12/15
12/15*60 = 48min
