How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

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Expert Solution

Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence

x + 40 = y

We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term.

20% x + 50% * 40 = 30% y

Substitute y by x + 40 in the last equation to obtain.

20% x + 50% * 40 = 30% (x + 40)

Change percentages into fractions.

20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100

Multiply all terms by 100 to simplify.

20 x + 50 * 40 = 30 x + 30 * 40

Solve for x.

x = 80 liters

Hence 80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.

Answer:80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.

Nipun Maity answered 2 years ago

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