Multiple choice

There are two vessels A & B in which the ratio of acid & water is 3 : 4 & 5 : 4 respectively. In which ratio both mixtures are mixed that in new mixture, there is half acid & half water?

  1. 3 : 7

  2. 7 : 11

  3. 9 : 10

  4. 7 : 9

  5. None of these

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the mixing ratio be a:b. Vessel A has acid ratio 3/7, Vessel B has acid ratio 5/9. For the final mixture to have 50% acid (ratio 1:1), use allegation: (3/7)(a) + (5/9)(b) = 1/2(a+b). Solving: 3a/7 + 5b/9 = (a+b)/2. Multiply by 126: 54a + 70b = 63a + 63b. So 70b - 63b = 63a - 54a, or 7b = 9a. Thus a/b = 7/9. Option D (7:9) is correct. Options A, B, and C don't satisfy the equation.