Multiple choice

Rahul mixes a 20% alcohol solution and a 30% alcohol solution in the respective ratio of c : d. The new solution thus obtained is mixed with an equal quantity of a 60% alcohol solution to obtain a 42% alcohol solution. Which among the following represents the ratio c : d?

  1. 4 : 1

  2. 3 : 2

  3. 5 : 2

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the ratio be c:d. The mixture of the first two is (0.2c + 0.3d)/(c+d). Mixing this with an equal quantity of 60% solution: [(0.2c + 0.3d)/(c+d) + 0.6] / 2 = 0.42. Solving this yields 0.2c + 0.3d + 0.6c + 0.6d = 0.84c + 0.84d, which simplifies to 0.04c = 0.06d, or c/d = 6/4 = 3/2.

AI explanation

When the initial mix of c and d is combined with an equal amount of 60 percent solution, the equation becomes (20c + 30d) divided by (c + d) plus 60, all divided by 2, equaling 42. This simplifies to 20c + 30d divided by (c + d) equaling 24. Multiplying through by (c + d) gives 20c + 30d = 24c + 24d, which simplifies to 6d = 4c. Therefore, the ratio of c to d is 6 to 4, which reduces to 3 : 2.

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