Multiple choice

A vessel contains a mixture of two liquids A and B in the ratio 2 : 3. When 8 liters of the mixture is taken out and replaced with B, the ratio of A and B becomes 6 : 11. How much of the mixture was there initially?

  1. 30 liter

  2. 68 liter

  3. 45 liter

  4. 64 liter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial mixture be x liters. Initial A = 2x/5, B = 3x/5. Removing 8L removes A = 16/5 L, B = 24/5 L. After adding 8L of B: new A = 2x/5 - 16/5, new B = 3x/5 - 24/5 + 8. New ratio (2x - 16)/(3x + 16) = 6/11. Solving: 22x - 176 = 18x + 96, so 4x = 272, x = 68L. Option A is incorrect. Option C would give ratio 6:13. Option D would give ratio 6:12.

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