Multiple choice

In three containers of Alcohol 10L capacity, mixture of alcohol and water is filled. The ratio of alcohol and water are 2 : 1, 3 : 1 and 3 : 2 in the respective vessels. If all the three vessels are emptied into a single large vessel, find the ratio of alcohol and water in the resultant mixture.

  1. 121:63

  2. 122:59

  3. 121:59

  4. 121:95
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total alcohol = 10*(2/3) + 10*(3/4) + 10*(3/5) = 20/3 + 30/4 + 30/5 = 6.66 + 7.5 + 6 = 20.16. Total water = 10*(1/3) + 10*(1/4) + 10*(2/5) = 3.33 + 2.5 + 4 = 9.83. Ratio = 20.16 / 9.83. Using fractions: (400+450+360)/60 : (200+150+240)/60 = 1210/60 : 590/60 = 121:59.

AI explanation

In each of the three 10 litre vessels, the amounts of alcohol are 2/3 of 10, 3/4 of 10 and 3/5 of 10, which equals 20/3, 15/2 and 6 litres respectively. The amounts of water in the three vessels are 10/3, 5/2 and 4 litres respectively. The total alcohol in the new 30 litre mixture is 20/3 + 15/2 + 6 = 121/6 litres, and the total water is 10/3 + 5/2 + 4 = 59/6 litres. The ratio of alcohol to water is therefore 121/6 to 59/6, which simplifies to 121 to 59.

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