Three bottles of equal capacity have mixture of milk and water in ratio 5 : 7, 7 : 9 and 2 : 1 respectively. These three bottles are emptied into a large bottle. What is the percentage of milk in the new mixture?
50.7
Step 1 — Choose a common capacity: LCM of (5+7), (7+9), (2+1) = LCM(12,16,3) = 48 units per bottle.
Step 2 — Milk in each bottle:
\[\tfrac{5}{12}\times 48=20,\quad \tfrac{7}{16}\times 48=21,\quad \tfrac{2}{3}\times 48=32\]
Step 3 — Percentage of milk:
\[\frac{20+21+32}{48\times 3}\times 100=\frac{73}{144}\times 100\approx 50.7\%\]
Therefore the new mixture is 50.7% milk.
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