How to solve Alligation and mixture shortcut How much water must be added to $60$ litres of milk at $1.5$ litres for Rs. $20$ so as to have a mixture worth Rs.$10 \frac{2}{3}$ a litre?

Assuming that water is free and $x$ liter water is required

the price of $60$ liter milk is $\displaystyle60\cdot\frac{20}{1.5} \ \ \ \ (1)$ RS.

Now we have diluted milk of $60+x$ liter with rate $\displaystyle=\frac{10}{\dfrac23}$ RS./liter

So, the total price will be $\displaystyle (60+x)\frac{10}{\dfrac23}$ which must be same as $(1)$