My Scooty gives an average of 40 kmpl of petrol. But after recent filling at the new petrol pump, its average dropped to 38 kmpl. I investigated and found out that it was due to adulterated petrol. Petrol pimps add kerosene, which is $$\frac{2}{3}$$  cheaper than petrol, to increase their profits. Kerosene generates excessive smoke and knocking and gives an average of 18 km per 900 ml. If I paid Rs. 30 for a litre of petrol, What was the additional amount the pump-owner was making?

Solution(By Examveda Team)

Let x ml of kerosene be there in 1 litre mixture.
Then, quantity of petrol in 1 litre mixture = (1000 - x) ml
$$\therefore \frac{{40}}{{1000}}\left( {1000 - x} \right)$$   $$ + \frac{{18}}{{900}}x$$   = 38
$$\eqalign{ & \Rightarrow \frac{x}{{25}} - \frac{x}{{50}} = 2 \cr & \Rightarrow \frac{x}{{50}} = 2 \cr & \Rightarrow x = 100 \cr} $$
So, 1 litre mixture has 900 ml petrol and 100 ml kerosene.
Cost of 1 litre petrol = Rs. 30
Cost of 1 litre kerosene
= Rs. $$\left[ {\left( {1 - \frac{2}{3}} \right) \times 30} \right]$$
= Rs. 10
Coast of 1 litre mixture
= Rs. $$\left( {\frac{{30}}{{1000}} \times 900 + \frac{{10}}{{1000}} \times 100} \right)$$
= Rs. 28
∴ Additional amount earned by pump-owner
= Rs. (30 - 28)
= Rs. 2