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: Quantity I: A mixes milk and sugar in an empty container in the ratio of 4: 9, respectively. If 39 litres of mixtures is taken out and 4 litres of sugar is mixed, then the ratio of milk and sugar becomes 3: 7, respectively. Find the amount of milk mixed initially. Quantity II: A tank contains mixture of water and alcohol in the ratio of 3: 7, respectively. 40 litres of mixture is sold and 4 litres of alcohol is mixed in the container. If the ratio of water and alcohol in container becomes 2: 5, then find the difference between the amount of water and alcohol present in the container initially.

  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 relationship cannot be established

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

Quantity I: Let milk=4x, sugar=9x. After removing 39 litres (4/13 milk, 9/13 sugar) and adding 4 litres sugar: (4x-12)/(9x-27+4) = 3/7. Solving: 7(4x-12) = 3(9x-23), 28x-84 = 27x-69, x=15. So milk=60 litres. Quantity II: Let water=3x, alcohol=7x. After selling 40 litres (3/10 water, 7/10 alcohol) and adding 4 alcohol: (3x-12)/(7x-28+4) = 2/5. Solving: 5(3x-12) = 2(7x-24), 15x-60 = 14x-48, x=12. So water=36, alcohol=84, difference=48. Therefore Quantity I (60) > Quantity II (48). Answer B is correct.