A 100 litre vessel contains water and milk in the ratio 2 : 3 and a 50 litre vessel contains water and milk in the ratio 3 : 2. If the contents of these vessels are mixed in the ratio 1 : 3 in a third vessel, what will be the respective ratio of milk to water in the third vessel? a) 12 : 13 b) 9 : 11 c) 11 : 9 d) 13 : 12

So water in the first vessel is 40 litres and milk is 60 litres.
In the second vessel, water is 30 litres and milk is 20 litres.
Now to mix them in ratio of 1:3, lets take capacity of vessel 3 as 400 litres.
In this we have 100 litres from vessel 1 and 300 litres from vessel 2.
So total milk in vessel 3 = 60 (V1) + {20 X 6} (V2) = 180 litres.
Remaining is water i.e. 400 - 180 = 220 litres.
Therefore ratio of milk to water in V3 is 9:11.
Hence option (b) is the answer.