Question

The ratio of milk and water in a mixture is 3:2. We
withdraw 25 lt mixture and added 15 It water to the
mixture, then ratio becomes 3: 7. Find the initial
quantity of milk.​

Answer 1

The ratio of milk & water in a vessel is 3:2. If 25 L mixture is drawn off and 15 L water is added then the ratio becomes 3:7. What was the initial quantity of the mixture?

Coding courses with basic to advance concepts.

Let the initial quantity of mixture be x with milk:water = 3:2

Amount of milk in the mixture = 3/5 x and water = 2/5 x

When 25 L of mixture is removed, amount of milk left = 3/5 x - 3/5 * 25 = 3/5 x - 15

Amount of water left = 2/5 x - 2/5 * 25 = 2/5x - 10

Amount of water after 15 more litres of water is added = 2/5x -10+15 = 2/5x + 5

Ratio of milk to water = 3/5x - 15 : 2/5 x + 5 = 3:7

(3/5x - 15)/(2/5 x +5) = 3/7

Cross multiply

21/5 x -105 = 6/5 x + 15

21/5 x - 6/5x = 15 +105

3x = 120

x = 40 L

Initial quantity of mixture = 40 L

Check:

In 40 L of initial mixture, milk = 40*3/5 = 24 L and water = 16 L

Amount of milk left when 25 L of mixture is removed = 24 - 3/5 * 25 = 24 - 15 = 9 L

Amount of water left after 25 lit of mixture is removed = 16 - 2/5 * 25 = 6 L

Amount of water after adding 15 L of water = 6 + 15 = 21L

Milk to water ratio in the new mixture = 9:21 = 3:7