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A water tank has inlets of two types A and B. All inlets of type A whe

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A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 07 Apr 2020, 08:29
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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


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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 07 Apr 2020, 09:08
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).
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 07 Apr 2020, 16:06
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
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 07 Apr 2020, 21:54
fireagablast wrote:
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


Hi could you explain why you've taken the equation as 10/a + 45/b and 8/a + 18/b. I am taking it as 10A+45B AND 8A+18B.. not able to get an answer though.
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 10 Apr 2020, 02:40
1
Bunuel wrote:
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


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If we let a and b, respectively, be the number of minutes it takes a type A and a type B inlet to fill the tank completely, then 1/a and 1/b are the rates of a type A and a type B inlet, respectively. We can create the equations:

10(1/a) + 45(1/b) = 1/30 → 10/a + 45/b = 1/30

and

8(1/a) + 18(1/b) = 1/60 → 8/a + 18/b = 1/60

If we multiply the second equation by -2, we have: -16/a - 36/b = -1/30. Adding this to the first equation, we have:

-6/a + 9/b = 0

9/b = 6/a

9a = 6b

b = 9a/6 = 3a/2

Now, substitute this back to the first equation and solve for a:

10/a + 45/(3a/2) = 1/30

10/a + 90/(3a) = 1/30

Multiplying both sides by 30a, we have:

300 + 900 = a

1200 = a

Therefore, b = 3(1200)/2 = 1800.

Thus, the combined rate of 7 type A and 27 type B inlets is 7 x (1/1200) + 27 x (1/1800) = 7/1200 + 3/200 = 7/1200 + 18/1200 = 25/1200. Since time is the inverse of rate, the time is 1200/25 = 48 minutes.

Answer: E
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 10 Apr 2020, 23:31
Bunuel wrote:
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


Given:
1. A water tank has inlets of two types A and B.
2. All inlets of type A when open, bring in water at the same rate.
3. All inlets of type B, when open, bring in water at the same rate.
4. 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.

Asked: 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?

Let inlets A & B fill the water tank in x hours and y hours respectively

The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open

10/(2x) + 45/(2y) = 1

5/x + 45/2y = 1

The empty tank is completely filled in 1 hour if 8 inlets of type A and 18 inlets of type B are open.

8/x + 18/y = 1

5/x + 45/2y = 8/x + 18/y
3/x = 9/2y
6y = 9x
2y = 3x
y = 1.5x

8/x + 18/1.5x = 1
20/x = 1
x = 20
y = 30

In minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open

7/20 + 27/30 = 7/20 + 9/10 = 25/20 = 5/4

Time needed = 4/5 hours = 48 minutes

IMO E
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 10 Apr 2020, 23:32
Kritisood wrote:
fireagablast wrote:
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


Hi could you explain why you've taken the equation as 10/a + 45/b and 8/a + 18/b. I am taking it as 10A+45B AND 8A+18B.. not able to get an answer though.



Hi Kritisood
Please check my answer and provide feedback.
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 12 Apr 2020, 22:07
Kinshook wrote:
Kritisood wrote:
fireagablast wrote:
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


Hi could you explain why you've taken the equation as 10/a + 45/b and 8/a + 18/b. I am taking it as 10A+45B AND 8A+18B.. not able to get an answer though.



Hi Kritisood
Please check my answer and provide feedback.


Understood, thanks a lot :)
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Re: A water tank has inlets of two types A and B. All inlets of type A whe  [#permalink]

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New post 12 Apr 2020, 22:28
2
1
Bunuel wrote:
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


The video explains a general principle (with derivation) and 2 step method to answer the problem


Answer: Option E


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Re: A water tank has inlets of two types A and B. All inlets of type A whe   [#permalink] 12 Apr 2020, 22:28

A water tank has inlets of two types A and B. All inlets of type A whe

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