A vessel is filled with liquid, 3 parts of which are water and 5 parts are syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

\(\frac{1}{5}\)

                                    Water               Syrup        Total

initial Ratio                       3          :          5      =        8

Ratio after drawn off        3          :          5      =        8 ........(i)

Ratio after water added   1          :          1      =        2 ........(ii)

In (i) and (ii) syrup should be same because in these steps only water is added. Therefore, (ii) × 5

                                      Water               Syrup        Total

Ratio after drawn off         3          :          5      =        8

Ratio after water added   5          :           5      =      10

                                        + 2                                    10 (Final/initial Qty.

Mixture to be removed = \(\frac{2}{10}\) = \(\frac{1}{5}\)