Miss Sanchez made 12 quarts of mango juice which contained 20% mango concentrate. How much water would she have to add to reduce it to 15% mango concentrate? Show solution

Question

Another question. How many liters of alcohol must be added to 40 liters of a mixture which is 65% alcohol to obtain a mixture which is 80% alcohol? Show solution

Answer 1

Answer 1)

Initial amount of the solution = 12 quarts

Amount of mango in juice is 20% of 12 quarts = 2.4  quarts

And mango concentrate is 15% of Y ml solution, where Y is new total of mango concentrate and water, after water being added to the solution.

So,

Y * 15% = 2.4     [Since, the amount of mango concentrate remains same]

=> Y = 2.4 * 100 / 15 = 16

So the amount of water added is New Amount - Old Amount = 16 -12 =4 quarts

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Answer 2)

Initial amount of the solution = 40 litres

Amount of alcohol in solution is 65% of 40 litres = 26 litres

So, the amount of water = 40 -26 = 14 litres

And water is 20% of Y ml solution, where Y is new total of alcohol and water, after alcohol being added to the solution.

So,

Y * 20% = 14     [Since, the amount of water remains same]

=> Y = 14 * 100 / 20 = 70

So the amount of alcohol added is New Amount - Old Amount = 70 - 40 = 30 litres

Answer 2

(1)

20% of 12 quarts of mango juice contains 12/5=2.4 quarts of concentrate and 12-2.4=9.6 quarts of water.

If we add x quarts of water the total juice contains 12+x quarts, made up of 2.4 quarts of concentrate and 9.6 quarts of water. So 2.4/(12+x)=15% or 0.15, 2.4=0.15(12+x)=1.8+0.15x, 2.4-1.8=0.15x, 0.6=0.15x, x=0.6/0.15=4 quarts. (2.4/16=15%)

(2)

0.65 of 40L=26L of pure alcohol. If we add x litres of alcohol the mixture will increase to 40+x and (26+x)/(40+x)=0.8, 26+x=32+0.8x, x-0.8x=32-26, 0.2x=6, x=6/.2=30L of alcohol. (56/70=80%)