Question

In a milk and water solution, the ratio of milk and water is 3 : 1. If 20 litres of mixture is taken out and 9 litres milk is added to the mixture then the percentage water in the mixture becomes 14$\frac{2}{7}$%. What is the total volume of the initial mixture?

Answer 1

Answer:

Step 1:

Let the initial quantity of milk be “3x” litres and the initial quantity of water be “x” litres.

So, the total volume of the initial mixture will be = 3x+ x = 4x …. (i)  

Step 2:

The percentage of water in the new mixture is given = 14$\frac{2}{7}$ %  

Then, the parts of water in the new mixture = [100/7] * [1/100] = 1/7

∴ The parts of milk in the new mixture = 1 – 1/7 = 6/7

∴ The ratio of milk and water in the new mixture = 6:1 …. (ii)

Step 3:

Since 20 litres of mixture is taken out and 9 litres milk is added to the mixture, so, the equation can be written as,

[3x – {(3/4)*20} + 9] / [x – {(1/4)*20}] = 6/1

⇒ [3x – 15 + 9] / [x - 5] = 6

⇒ 3x – 6 = 6x – 30

⇒ 3x = 24

⇒ x = 8

Step 4:

Thus, substituting x = 8 in (i), we get

The total volume of the initial mixture as,

= 4x

= 4 * 8

= 32 litres