Question

$\text{Sam, a dishonest milkman, waters down the}\text{milk he sells at}\$36\text{a day. If he sells the}\text{milk pure, he can only sell it for}\$30\text{. If so,}\text{how much water does Sam add to 1 gallon of}\text{pure milk?}$

• A. 0.25 gal
• B. 0.15 gal
• C. 0.2 gal
• D. 0.1 gal

Answer 1

The correct option is C 0.2 gal

We take:

$Volumeofpuremilk=M$
$Volumeofwateradded=W$

Now, the money earned is always proportional to the volume that is sold.

So, taking 'k' as the proportionality constant, we have:

$Moneyearnedsellingwatereddownmilk=k\times (M+W)⟹k\times (M+W)=\$\mathrm{36....}Equation1$

Similarly,

$Moneyearnedsellingpuremilk=k\times M⟹k\times M=\$\mathrm{30......}Equation2$

Dividing equation (1) by equation (2), we get:

$\frac{k\times (M+W)}{k\times M}=\frac{\$36}{\$30}$

$⟹[1+\frac{W}{M}]=[1+\frac{6}{30}]$

$⟹\frac{W}{M}=\frac{6}{30}=\frac{1}{5}$

$⟹W=\frac{M}{5}$

So, for 1 gallon of milk, the volume of water added will be:

$W=\frac{1}{5}=0.2gal$