Three containers A, B, and C are having mixtures of milk and water in the…
2024
Three containers A, B, and C are having mixtures of milk and water in the ratio of 1:5, 3:5, 5:7 respectively. If the capacities of the containers are in the ratio 5:4:5, find the ratio of milk to water, if all the three containers are mixed together.
- A.
53:115
- B.
53:113
- C.
54:115
- D.
54:113
Attempted by 236 students.
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Correct answer: A
Solution: Find milk and water amounts from each container using capacities proportional to 5:4:5.
First container (capacity proportional to 5), ratio milk:water = 1:5:
Milk = 5 × (1/(1+5)) = 5 × 1/6 = 5/6; Water = 5 × (5/6) = 25/6.
Second container (capacity proportional to 4), ratio milk:water = 3:5:
Milk = 4 × (3/(3+5)) = 4 × 3/8 = 12/8; Water = 4 × 5/8 = 20/8.
Third container (capacity proportional to 5), ratio milk:water = 5:7:
Milk = 5 × (5/(5+7)) = 5 × 5/12 = 25/12; Water = 5 × 7/12 = 35/12.
Total milk = 5/6 + 12/8 + 25/12 = 10/12 + 18/12 + 25/12 = 53/12.
Total water = 25/6 + 20/8 + 35/12 = 50/12 + 30/12 + 35/12 = 115/12.
Check: combined total = 53/12 + 115/12 = 168/12 = 14, which equals the sum of capacities 5+4+5.
Final answer: 53:115