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?

Let the capacity of each bottle = 48 litres    [L.C.M.(12,16,3)]

Ratio of milk and water in the three bottles respectively = 5:7 , 7:9 , 2:1

Milk in 1st bottle = $$\frac{5}{(5+7)}\times48=20$$ litres

and water in 1st bottle = $$48-20=28$$ litres

Similarly, milk in 2nd bottle = $$\frac{7}{16}\times48=21$$ litres

 and water in 2nd bottle = $$48-21=27$$ litres

Similarly, milk in 3rd bottle = $$32$$ litres and water = $$16$$ litres

=> Total milk = $$20+21+32=73$$ litres

 and total water = $$28+27+16=71$$ litres

$$\therefore$$ Percentage of milk in the new mixture = $$\frac{73}{(73+71)}\times100$$

= $$\frac{7300}{144}=50.69 \approx 50.7\%$$

=> Ans - (D)