Question

4) The proportion of milk and water in three samples is 2:1, 3:2 and 5:3. A mixture comprising equal quantities of all three samples is made. The proportion of milk and water in the mixture is?​

Answer 1

milk : water = 227 : 133

Explanation:

The proportion of milk in the whole will be the weighted sum of the proportions in each of the samples. The weighting will be the proportion of each sample in the whole.

Proportions of milk

We are given the ratios in the form of ...

milk : water

What we want to average are the ratios in the form of ...

milk : whole = milk : (milk +water)

These three proportions are ...

2:1 milk : water ⇒ 2 : 3 milk : whole

3:2 milk : water ⇒ 3 : 5 milk : whole

5:3 milk : water ⇒ 5 : 8 milk : whole

Proportion in mix

The weighted average of these proportions is ...

(1/3)(2/3) +(1/3)(3/5) +(1/3)(5/8) . . . . . each gets a weight of 1/3

= 2/9 +1/5 +5/24

Using a common denominator, the sum is ...

= 80/360 +72/360 +75/360 = 227/360 (milk : whole)

The ratio we want is ...

milk : water = milk : (whole -milk) = 227 : (360 -227)

milk : water = 227 : 133 . . . . proportion in the mix of samples