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10 May 2018, 22:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (02:07) correct
25%
(02:28)
wrong
based on 304
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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
A. 1 litre
B. 1.5 litre
C. 2 litres
D. 2.5 litres
E. 3 litres
10 May 2018, 22:59
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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.
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.
General Discussion
10 May 2018, 23:02
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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.
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.
