Multiple choice

The ratio of alcohol to water in two containers, A and B, are 5 : 3 and 1 : 3, respectively, with both containers having infinite capacity. Suppose that the aim is to obtain 2.1 litre of liquid which is composed of equal quantities of alcohol and water. How much liquid should be drawn from A?

  1. 1.4 litre

  2. 1.05 litre

  3. 0.35 litre

  4. 1.1 litre
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the amount from A and y be the amount from B. x + y = 2.1. Alcohol content: (5/8)x + (1/4)y = 1.05. Substitute y = 2.1 - x: (5/8)x + (1/4)(2.1 - x) = 1.05. (5/8 - 2/8)x = 1.05 - 0.525. (3/8)x = 0.525. x = 0.525 * 8 / 3 = 1.4.

AI explanation

Container A has alcohol and water in a 5 to 3 ratio, so it contains 5 parts alcohol out of 8 total parts, or 5/8 alcohol. Container B has a 1 to 3 ratio, so it contains 1/4 alcohol. Using the rule of alligation on the alcohol fractions, we get 1/2 minus 1/4 equals 1/4 for A, and 5/8 minus 1/2 equals 1/8 for B. The ratio of A to B to be drawn is 1/4 to 1/8, which simplifies to a 2 to 1 ratio. To make 2.1 litres total, the amount from A is 2.1 times 2/3, which is 1.4 litres.

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