A container contains milk and water in the ratio of 7 : 5 respectively. 9 liters of mixture is drawn off and replaced by water, there after ratio of milk and water becomes 7 : 9. Find original quantity of the milk in the mixture.

21 liters

Milk   :    Water

  7     :      5

In 9 liters mixture

Milk = \(\frac{9}{12}\) × 7 = \(\frac{21}{4}\) liters

Water = \(\frac{9}{12}\) × 5 = \(\frac{15}{4}\) liters

ATQ,

\(\frac{7x - \frac{21}{4}}{5x - \frac{15}{4} + 9}\) = \(\frac{7}{9}\)

63x - \(\frac{189}{4}\) = 35x + \(\frac{147}{4}\)

28x = \(\frac{189}{4}\) + \(\frac{147}{4}\) = \(\frac{336}{4}\) = 84

x= \(\frac{84}{28}\) = 3

Original quantity of milk = 7x = 7 × 3 = 21 liters