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

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

Solution:
let, milk 6x, water = 5x
total = 6x + 5x
= 11x

When 44 litre of mixture is replaced with water, then remaining milk is = 6x - 22 × 6/11
= 6x - 12

remaining water = 5x - 22 × 5/11 + 22
= 5x - 10 + 22
= 5x + 12

(6x - 12)/(5x + 12) = 9/13
⇒ 78x - 13 × 12 = 45x + 9 × 12
⇒ 78x - 45x = 9 × 12 + 13 × 12
⇒ 33x = 9 × 12 + 13 × 12
⇒ x = 12 × 22/33
= 8

quantity of milk after replacement = 6 × 8 - 12
= 48 - 12
= 36 litre