A 729 ml mixture contains milk and water in the ratio 7 : 2. How much water…
2022
A 729 ml mixture contains milk and water in the ratio 7 : 2. How much water must be added to obtain a new milk-to-water ratio of 7 : 3?
Answer: A. 81 ml — ConceptWhen only water is added to a mixture, the amount of milk remains unchanged; only the water quantity increases. In a ratio a : b, the total is divided…
- A.
81 ml
- B.
90 ml
- C.
85 ml
- D.
75 ml
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept
When only water is added to a mixture, the amount of milk remains unchanged; only the water quantity increases.
In a ratio a : b, the total is divided into a + b equal parts, and the component quantities are proportional to a and b.
Application
The initial ratio has 7 + 2 = 9 parts, so one part is 729 / 9 = 81 ml.
Initial milk = 7 × 81 = 567 ml, and initial water = 2 × 81 = 162 ml.
Let x ml of water be added. The new water quantity is 162 + x ml, while milk remains 567 ml.
The target ratio gives 567 / (162 + x) = 7 / 3.
Cross-multiplying gives 3 × 567 = 7 × (162 + x). Therefore, 1701 = 1134 + 7x, so 7x = 567 and x = 81 ml.
Cross-check
After adding 81 ml, water becomes 162 + 81 = 243 ml. The ratio 567 : 243 reduces to 7 : 3.
Therefore, the required quantity of water to be added is 81 ml.