In a mixture, the ratio of milk and water is 6 : 5. When 22 liter mixture is replaced by water, the ratio become 9 : 13. Find the quantity of water after replacement.

Question: In a mixture, the ratio of milk and water is 6 : 5. When 22 liter mixture is replaced by water, the ratio become 9 : 13. Find the quantity of water after replacement.

Solution:
Let milk = 6X, water = 5X
so,
total mixture = 6X + 5X = 11X

When 22 liter of mixture is replaced with water, then remaining milk is = 6X - (22 × 6X/11X) = 6X - 12

remaining water = 5X - (22 × 5X/11X) + 22 = 5X + 12

ATQ,
6X - 12 : 5X + 12 = 9 : 13
13(6X - 12) = 9(5X + 12)
78X - 156 = 45X + 108
78X - 45X = 156 + 108
33X = 164
X = 8

∴ water after replacement = 5X + 12 = 40 + 12 = 52 liters