In a container the ratio of mixture of milk and water is 5 : 2. If 10 litres of water is added to the mixture, then the difference between milk and water becomes 20 litres. Find the initial quantity of mixture.

Given:

The initial ratio of milk and water is 5 : 2.

10 litres of water is added to the mixture.

The difference between the quantity of milk and water becomes 20 litres.

Let the initial quantity of the mixture be X litres.

Calculation:

Since the ratio of milk to water is 5:2, we can say:

Milk = (5 / 7) × X

Water = (2 / 7) × X

After adding 10 litres of water, the new quantity of water becomes:

Water = (2 / 7) × X + 10

The difference between the amount of milk and water is given as 20 litres:

Milk - Water = 20

Substitute the values for milk and water:

(5 / 7) × X - [(2 / 7) × X + 10] = 20

Now, simplify the equation:

(5 / 7) × X - (2 / 7) × X - 10 = 20

(3 / 7) × X - 10 = 20

Now, add 10 to both sides:

(3 / 7) × X = 30

Now, multiply both sides by 7/3:

X = (30 × 7) / 3

X = 70

∴ The initial quantity of the mixture is 70 litres.