A bucket contains a mixture of milk and water in the proportion of 7: 5. If 9 litres of milk is replaced by water, then the ratio becomes 7:9. How much milk was there in the bucket initially?

Correct option is A

Given:
Ratio of the mixture of milk and water = 7 : 5
When 9 litres of milk is replaced by water, then the ratio becomes 7 : 9.
Solution:
Let the amount of milk be 7x and water be 5x in the mixture.
Total mixture = 7x + 5x = 12x litres
Amount of milk after reduction = 7x – 9
Amount of water after reduction = 5x + 9
Now, the ratio becomes 7:9, so
​$$\frac{(7x-9)}{(5x+9)}=\frac{7}{9}$$​​
Cross multiplies the terms, we get
9(7x – 9) = 7(5x + 9)
63x – 81 = 35x + 63
63x – 35x = 63 + 81
28x = 144
x = $$\frac{144}{28}=\frac{36}{7}$$​​
Initial amount of milk in bucket = 7x = 7×$$\frac{36}{7}$$​=36 litres