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A mixture of 70 litres of alcohol and water contains 10% of water. How

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A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 10 May 2018, 22:47
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A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?


A. 1 litre

B. 1.5 litre

C. 2 litres

D. 2.5 litres

E. 3 litres

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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 10 May 2018, 22:59
Choice C: 2 litres

The initial mixture contains 10% water out of the total 70 litres.
So, the initial mixture has 7 litres water and 63 litres alcohol.

What is done? Only water is added and after that the concentration of water becomes 12.5%
Fractional equivalent of 12.5% = 1/8

Method 1: Let x litres of water be added to the mixture.
So, we will have (7 + x) litres of water and (70 + x) litres of mixture finally.
Because 12.5% or 1/8 of the total mixture is water, (7 + x)/(70 + x) = 1/8
8(7 + x) = 70 + x
56 + 8x = 70 + x
Or 7x = 14
So, x = 2.

Method 2: The quantity of alcohol remains unchanged at 63 litres in the initial and final mixture.
After adding water, the new mixture will have 1/8 water or 7/8th of the new volume will be alcohol.
If 7/8th of the new volume = 63, new volume = 63 * (8/7) = 9 * 8 = 72 litres.

Initial volume = 70 litres. New volume = 72 liters.
Water added = 2 litres.
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 10 May 2018, 23:02
Original Alcohol percentage = 90% = 0.9*70 = 63 litres
Original Water percentage = 10% = 0.1*70 = 7 litres

New Alcohol percentage = 87.5% = 63 litres .
1% percentage = \(\frac{63}{87.5}\) = 0.72 litre
New water percentage =12.5% = 0.72*12.5 = 9 litres

How much water to be added = 9-7 = 2litres

Hence option C = 2 litres is the answer.
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 11 May 2018, 01:30
Bunuel wrote:
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?


A. 1 litre

B. 1.5 litre

C. 2 litres

D. 2.5 litres

E. 3 litres


The quantity of alcohol should not change. Total quantity of given mixture is - 70 litres.

In the given mixture, the 10% water corresponds to 7 litres of water.

In the given mixture, the 90% alcohol corresponds to 63 litres of alcohol.

After adding water, the new mixture will have 12.5% water implies 1/8 water and 7/8th part of mixture will be alcohol.

Because alcohol quantity will remain same, 7/8th of Volume of new mixture = 63.

Volume of new mixture = 63 * (8/7) = 9 * 8 = 72 litres.

Initial volume = 70 litres. New volume = 72 liters.

Water added = 2 litres.
Ans - C
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 11 May 2018, 02:16
Volume of water in the given mixture = 70* 10%= 7 litres
Let the volume of water added= x
Concentration of water in the final solution= 12.5%

We know that, Concentration of water in final solution= (Volume of water/ Total volume) *100

{(7 + x)/ (70 + x )} *100 = 12.5
700 + 100 x= 12.5(70 + x)
12.5 x -100x = 700 - 12.5 *70
- (87.5)x = - 175
x = 2

Correct Answer= C
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 11 May 2018, 10:26
Bunuel wrote:
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?


A. 1 litre

B. 1.5 litre

C. 2 litres

D. 2.5 litres

E. 3 litres


let w=water to be added
7+w=.125(70+w)
w=2 litres
C
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 11 May 2018, 10:35
Answer choice: C

Total = 70 liters

Water = (10/100)*70 = 7 liters

Let x be the amount of water added to make water as 12.5% in resultant mixture

So New Total = 70+x

New water = 7+x

12.5% = 1/8

Hence (1/8) * (70+x) = 7+x

Solving for x

x = 2 litres

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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 14 May 2018, 16:49
Bunuel wrote:
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?


A. 1 litre

B. 1.5 litre

C. 2 litres

D. 2.5 litres

E. 3 litres


We have 7 litres of water and 63 litres of alcohol.

We can create the equation in which w = water added:

(7 + w)/(70 + w) = 0.125

(7 + w)/(70 + w) = 125/100

(7 + w)/(70 + w) = 1/8

8(7 + w) = 70 + w

56 + 8w = 70 + w

7w = 14

w = 2

Answer: C
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How  [#permalink]

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New post 23 Jun 2018, 08:49
Bunuel wrote:
A mixture of 70 litres of alcohol and water contains 10% of water. How much water must be added to the above mixture to make the water 12.5% of the resulting mixture?


A. 1 litre

B. 1.5 litre

C. 2 litres

D. 2.5 litres

E. 3 litres



using weighted average method

let x litres of water is required to be added

\frac{70}{x} = \frac{(100-12.5)}{(12.5-10)}

solve for x = 2 ltrs
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Re: A mixture of 70 litres of alcohol and water contains 10% of water. How &nbs [#permalink] 23 Jun 2018, 08:49
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