Bunuel wrote:
A jar contains a mixture of 175 ml water and 700 ml alcohol. Randy takes out 10% of the mixture and substitutes it by water of the same amount. If the process is repeated once again, what will be the percentage of water in the mixture ?
A. 20.5
B. 25.4
C. 29.5
D. 30.3
E. 35.2
Are You Up For the Challenge: 700 Level Questions Solution:We see that the jar originally has 875 ml of the mixture. When Randy removes 10% (or 87.5 ml) of the mixture, he is removing 10% (or 17.5 ml) of water and 10% (or 70 ml) of alcohol. In other words, the jar has 175 - 17.5 = 157.5 ml of water and 700 - 70 = 630 ml of alcohol left. However, since he is replacing it with 87.5 ml water, the jar now has 157.5 + 87.5 = 245 ml of water and 630 ml of alcohol before the second replacement.
For the second replacement, he again removes 10% (or 87.5 ml) of the mixture, consisting of 10% (or 24.5 ml) water and 10% (or 63 ml) alcohol. In other words, the jar has 245 - 24.5 = 220.5 ml of water and 630 - 63 = 567 ml of alcohol left. However, since he is replacing it with 87.5 ml water, the jar now has 220.5 + 87.5 = 308 ml of water and 567 ml of alcohol after the second replacement. Therefore, the percentage of water in the mixture is 308/875 = 0.352 = 35.2%.
Alternate Solution:Notice that the amount of alcohol decreases by 10% in each step. Thus, after the first replacement, the amount of alcohol in the mixture is 700 * 0.9 = 630 ml, and after the second replacement, the amount of alcohol decreases to 630 * 0.9 = 567 ml.
Notice also that the amount of water added back to the solution is the same as the amount of mixture removed at each step; thus, the total amount of mixture is always 700 + 125 = 825 ml.
After the second replacement, there are 875 - 567 = 308 ml of water in the mixture, and the percentage of water in the mixture is 308/875 = 0.352 = 35.2%.
Answer: E