Multiple choice

A 30 litres mixture is made up of 2 components (C1 and C2) in the ratio 3 : 2. If some quantity of the mixture is taken out and 6 litres of C1 and 6 litres of C2 is added to the mixture, then the ratio of C1 and C2 becomes 6 : 5. What is the quantity of mixture which was taken out initially?

  1. 14 litres

  2. 20 litres

  3. 27 litres

  4. 32 litres

  5. 36 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 18L C1, 12L C2. Let x be the amount taken out. Remaining: (18 - 0.6x) C1, (12 - 0.4x) C2. Adding 6L of each: (24 - 0.6x) / (18 - 0.4x) = 6/5. Solving for x: 120 - 3x = 108 - 2.4x, 12 = 0.6x, x = 20.

AI explanation

Assume x liters of the mixture are taken out, meaning 3x/5 liters of C1 and 2x/5 liters of C2 are removed. The initial mixture has 18 liters of C1 and 12 liters of C2, so after removal and adding 6 liters of each component, the new ratio is (18 minus 3x/5 plus 6) to (12 minus 2x/5 plus 6) equals 6 to 5. Solving the equation 5 times (24 minus 3x/5) equals 6 times (18 minus 2x/5) gives 120 minus 3x equals 108 minus 2.4x, which results in x equal to 20 liters.

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