Question

In a vessel, milk and water are in a ratio of 3 : 5. In the second vessel, the milk and water are in the ratio of 3 : 2. In what ratio should these two mixtures be mixed to form a new mixture in which the milk and water are in the ratio 2 : 3?

1. 1 : 8
2. 6 : 1
3. 7 : 1
4. 8 : 1
5. None of these

Answer 1

Correct Answer - Option 4 : 8 : 1

Given:

The ratio of milk and water in the first vessel = 3 : 5

The ratio of milk and water in the second vessel = 3 : 2

The ratio of milk and water in the final mixture = 2 : 3

Concept used:

(New quantity of milk/New quantity of water) = (Quantity of milk taken from first vessel + Quantity of milk taken from the second vessel)/(Quantity of water taken from first vessel + Quantity of water taken from the second vessel)

Calculation:

Let the mixture from the two-vessel be mixed in the ratio x : y.

Quantity of milk taken from the first vessel = 3x/8

Quantity of water taken from the first vessel = 5x/8

Quantity of milk taken from the second vessel = 3y/5

Quantity of water taken from the second vessel = 2y/5

Then, {(3x/8) + (3y/5}/{(5x/8) + (2y/5)} = 2/3

⇒ {(15x + 24y)/40}/{(25x + 16y)/40} = 2/3

⇒ 3(15x + 24y) = 2(25x + 16y)

⇒ 45x + 72y = 50x + 32y

⇒ 50x – 45x = 72y – 32y

⇒ 5x = 40y

⇒ x/y = 8/1

∴ The first and second ratio is mixed in the ratio 8 : 1.