In the given question, two quantities are given, one as ‘Quantity I’ and…
2025
In the given question, 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 mixture contains 120 liters of milk and water in the ratio of 3:5, respectively. If Y liters of mixture are taken out and 10 liters of milk and 15 liters of water are added to the mixture, then the ratio of milk to water becomes 8:13. Find Y. Quantity II : 60
- A.
Quantity I > Quantity II
- B.
Quantity I < Quantity II
- C.
Quantity I ≥ Quantity II
- D.
Quantity I ≤ Quantity II
- E.
Quantity I = Quantity II or no relation
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
In a fixed mixture, both components are present in the same ratio everywhere, so when a portion is drawn off, milk and water leave in the SAME ratio as the original blend. The standard method: convert the starting ratio into actual quantities, remove the withdrawn part proportionally, add the new amounts, and set the resulting milk-to-water ratio equal to the target to solve for the unknown. A 'Quantity I vs Quantity II' item is then decided by comparing the two computed values.
Application
Starting amounts: 120 L in milk : water = 3 : 5, so milk = 120 x 3/8 = 45 L and water = 120 x 5/8 = 75 L.
Remove Y L of the mixture. Since the mixture is 3/8 milk and 5/8 water, milk removed = (3/8)Y and water removed = (5/8)Y, leaving milk = 45 - (3/8)Y and water = 75 - (5/8)Y.
Add 10 L milk and 15 L water: milk = 55 - (3/8)Y and water = 90 - (5/8)Y.
Target ratio milk : water = 8 : 13 gives 13(55 - (3/8)Y) = 8(90 - (5/8)Y).
Expand: 715 - (39/8)Y = 720 - (40/8)Y, so (40/8)Y - (39/8)Y = 720 - 715, i.e. (1/8)Y = 5, hence Y = 40.
So Quantity I = 40 and Quantity II = 60.
Cross-check
With Y = 40: milk = 55 - 15 = 40 L and water = 90 - 25 = 65 L, giving 40 : 65 = 8 : 13, which matches the target. Comparing 40 with 60, Quantity I is strictly less than Quantity II. Because Y is a single fixed value (40) and not 60, the comparison is determinate, so the strict 'less-than' relation is the answer rather than a non-strict (less-than-or-equal) one.