A mixture contains milk and water in the ratio (by volume) 5 : 3 and another mixture, of the same volume as that of the former, contains water and milk in the ratio (by volume) 1 : 3. In what ratio, two mixtures be mixed in order to obtain a new mixture consisting of milk and water in the ratio (by volume) 7 : 3 ?

2 : 3

Amount of milk in 1st mixture = \(\frac{5}{8}\)

Amount of milk in 2nd mixture = \(\frac{3}{4}\)

Amount of milk in the required solution = \(\frac{7}{10}\)

By allegation method,

⇒ Therefore, the required ratio = \(\frac{2}{40}\) : \(\frac{6}{80}\) = 2 : 3.