Question

Three jars of equal capacity are filled to the brim with milk-water solution, having milk and water in the ratios of 2 : 3, 1 : 3 and 3 : 5. if the contents of the three jars are emptied into a large vessel, then what is the ratio of milk to water in the vessel?

Answer 1

The three vessels are of equal capacity (which we assume to be full since it is a PS question). The milk:water ratio is given for each as 2:3, 1:3 and 3:5.
The reason we cannot just add the milk parts (2+1+3) and water parts (3+3+5) together is that they represent different fractions of the whole volume i.e. in the first vessel, milk is 2 parts out of a total of 5 parts while in the second vessel, milk is 1 parts out of a total of 4 parts. In the third we've milk 3 parts out of a total of 8 parts.
If we make the total number of parts in each ratio equal, then we can just add the 'milk parts' together and all the 'water parts' together.
Ratios:
2:3 (Total 5 parts)
1:3 (Total 4 parts)
3:5 (Total 8 parts)
How can we make the total number of parts equal in the 3 cases? By taking the LCM of {5, 4, 8}

(2x8):(3x8) = 16:24 (Total parts 40)
(1x10):(3x10) = 10:30 (Total parts 40)
(3x5):(5x5) = 15:25(Total parts 40)
When we mix the three solutions, the total number of parts of milk is 16+10+15 = 41
the total number of parts of water = 24+30+25 = 79
The required ratio = 41:79.
Hope you get the answer.
© Hades09