Question

A dishonest milkman a buys $100$ liters of milk from another dishonest milkman $B$ for onward distribution. He retains $10$ liter of milk for personal use, adds water to make up the shortfall and sells the mixture at Rs. $15$ /liter, there by making a profit of Rs. $2.75$ /liter on the quantity sold. If $B$ had already diluted the milk with water in the ratio of milk : water $9:1$ and he makes a profit of Rs. $1$, the price per liter of pure milk purchased by $B$ is closest to?

Answer 1

$A$ taken milk from $B$ $=100$ liters
B has milk and water in $9:1$ ratio i.e. $B$ sold $90$ liters milk and $10$ liters water to $A$ instead of $100$ liters milk.
A retain milk $=10$ liters ($9$ liters milk and $1$ liters water)
Now, $A$ has $90$ liters milk ($81$ liters milk and $9$ liters water) to sell and he has to add $10$ liters more water to make milk $100$ liters ($81$ milk $+$ $19$ water )
$B$ sells $15$ per/L with Rs. $2.75$ profit.
So, cost price of $A$ $=15-2.75=$ Rs. $12.25$
Cost price of $A$ for pure milk $\left(90\right)$ L $=\frac{100\times 12.25}{90}=$ Rs. $13.61$ per liter.