Henry Ernest Dudeney/Puzzles and Curious Problems/130 - Milk and Cream/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $130$

A dairyman found that the milk supplied by his cows was $5$ per cent cream and $95$ per cent skimmed milk.

He wanted to know how much skimmed milk he must add to a quart of whole milk to reduce the percentage of cream to $4$ per cent.

Half a pint.

Let $v_c$ be the volume of cream in a volume $v$ of whole milk.

Let $w$ be the quantity of skimmed milk needed to reduce the volume of cream to $4 \%$.

We have:

$\ds v_c$

$=$

$\ds \dfrac v {20}$

... $5$ per cent cream and $95$ per cent skimmed milk.

$\ds v_c$

$=$

$\ds \dfrac {v + w} {25}$

... reduce the percentage of cream to $4$ per cent.

$\ds \leadsto \ \ $

$\ds \dfrac v {20}$

$=$

$\ds \dfrac {v + w} {25}$

$\ds \leadsto \ \ $

$\ds 5 v$

$=$

$\ds 4 \paren {v + w}$

$\ds \leadsto \ \ $

$\ds w$

$=$

$\ds \dfrac v 4$

As we are told that $v$ is $1$ quart, it follows that the amount of skimmed milk to be added is half a pint.

$\blacksquare$