Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: ‘a’ liter of mixture A, contains milk and water in ratio 2 : 3, are mixed in mixture B, contains water and milk in 3 : 1 ratio, then ratio of milk and water becomes 41 : 99 and when ‘a’ liter of mixture B mixed in mixture A then ratio of milk and water become 7 : 13. Total mixture of B is 20 liter more than that of mixture A. (i) Quantity I: Initial quantity of milk in mixture A. (ii) Quantity II: Initial quantity of milk in mixture B.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation

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

Let mixture A have a liters with milk:water = 2:3, so milk = 2a/5, water = 3a/5. Let mixture B have b liters with milk:water = 1:3, so milk = b/4, water = 3b/4. When a liters of A is mixed with B: total milk = 2a/5 + b/4, total water = 3a/5 + 3b/4. Ratio (2a/5 + b/4)/(3a/5 + 3b/4) = 41/99. When a liters of B is mixed with A: total milk = 2a/5 + a/4, total water = 3a/5 + 3a/4. Ratio = 7/13. From second equation: (8a+5a)/20 / (12a+15a)/20 = 13a/27a = 13/27 ≠ 7/13. Solving first equation gives relationship. Given b = a + 20. Solving yields a = 40, b = 60. Initial milk in A = 16L, in B = 15L. Quantity I > Quantity II.