In a mixture of 42 litres the ratio of milk and water is 5:2. If 8 litres of…
2024
In a mixture of 42 litres the ratio of milk and water is 5:2. If 8 litres of water is added to the mixture, the ratio of milk to water in the resultant mixture will become :
- A.
1:2
- B.
3:2
- C.
2:1
- D.
2:3
Show answer & explanation
Correct answer: B
Concept: When a fixed quantity of one component is added directly to an existing mixture, the amount of every other original component stays exactly the same — only the added component's quantity changes. To find the new ratio between two components, first recover each component's actual quantity from the given ratio and total, then update only the quantity that changed.
Total mixture = 42 litres and the ratio of milk to water = 5 : 2, so the mixture divides into 5 + 2 = 7 equal parts.
Value of 1 part = 42 ÷ 7 = 6 litres.
Quantity of milk = 5 × 6 = 30 litres; quantity of water = 2 × 6 = 12 litres.
8 litres of water is added, so the new quantity of water = 12 + 8 = 20 litres, while the quantity of milk stays at 30 litres — the addition only affects water.
New ratio of milk to water = 30 : 20. Dividing both terms by their HCF, 10, gives 3 : 2.
Cross-check: the new total volume is 30 + 20 = 50 litres, which equals the original 42 litres plus the 8 litres added (42 + 8 = 50 litres) — confirming no quantity was missed in the recomputation.