A milkman purchases milk at ₹'a' per litre and sells it at ₹1.5a per litre. Still he mixes 2 litres water with every 9 litres of pure milk. What is his profit percentage?

A milkman purchases milk at ₹'a' per litre and sells it at ₹1.5a per litre.

cost price of each litre milk = ₹'a'

selling price of each litre milk = ₹'1.5a'

Still he mixes 2 litres water with every 9 litres of pure milk.

It means that he purchases 9 litres of pure milk and mix 2 litres water and sell 11 litres of mixture at the price of milk.

cost price of 9 litres milk = $$9\times a$$ = 9a    Eq.(i)

selling price of 11 litres mixture(milk+water) = $$11\times 1.5a$$ = 16.5a    Eq.(ii)

profit percentage = $$\frac{\left(Eq.(ii)-Eq.(i)\right)}{Eq.(i)}\times\ 100$$

= $$\frac{\left(16.5a-9a\right)}{9a}\times\ 100$$

= $$\frac{7.5a}{9a}\times100$$

= $$\frac{2.5}{3}\times100$$

= $$\frac{250}{3}$$%