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 pumps 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 ₹ 30 for a litre of petrol, what was the additional amount the pump-owner was making?

### Concept & Logic This problem requires a two-step approach: first using the **Rule of Alligation** to find the volumetric ratio of petrol to kerosene in the mixture, and then calculating the cost price of this mixture to determine the profit made by substituting cheaper fuel. ### Step-by-Step Solution * **Given:** * Original pure petrol average = $40$ km/L * Adulterated mixture average = $38$ km/L * Kerosene average = $18$ km per $900$ ml * Pure petrol cost = ₹ $30$ per Litre * Kerosene is $\frac{2}{3}$ cheaper than petrol. * **Calculation / Deduction:** 1. Find the per-litre average of kerosene: If it gives $18$ km for $900$ ml ($0.9$ L), then for $1000$ ml ($1$ L), it gives: $\frac{18}{0.9} = 20$ km/L. 2. Find the mixture ratio using alligation: Petrol average = $40$ Kerosene average = $20$ Mixture average = $38$ Ratio of Petrol to Kerosene = $(38 - 20) : (40 - 38) = 18 : 2 = 9 : 1$. This means in $1$ Litre of mixture, petrol is $\frac{9}{10}$ L and kerosene is $\frac{1}{10}$ L. 3. Calculate the cost price for the pump owner: Cost of pure petrol = ₹ $30$/L. Kerosene is $\frac{2}{3}$ cheaper, meaning its cost is reduced by $\frac{2}{3}$. Cost of kerosene = $30 - (\frac{2}{3} \times 30) = 30 - 20 =$ ₹ $10$/L. Cost of $1$ Litre of the adulterated mixture = (Cost of $\frac{9}{10}$ L petrol) + (Cost of $\frac{1}{10}$ L kerosene) Mixture Cost = $(\frac{9}{10} \times 30) + (\frac{1}{10} \times 10) = 27 + 1 = $ ₹ $28$. 4. Calculate the additional amount made: He sells it at the pure petrol price (₹ $30$) but his actual cost is ₹ $28$. Additional amount = $30 - 28 = $ ₹ $2$. ### Exam Strategy & Shortcut Standardize all your units first (convert $900$ ml to $1$ Litre immediately). Once you use alligation to find the $9:1$ ratio, simply calculate the cost difference per portion. The owner replaces $\frac{1}{10}$ of ₹ $30$ petrol with ₹ $10$ kerosene. The savings (extra profit) is exactly $\frac{1}{10}$ of the price difference between the two fuels: $\frac{1}{10} \times (30 - 10) = \frac{20}{10} = $ ₹ $2$. ### Common Pitfall Students often misinterpret "$\frac{2}{3}$ cheaper" as meaning the cost is $\frac{2}{3}$ of the original. "Cheaper by" implies subtraction, so the actual cost is $1 - \frac{2}{3} = \frac{1}{3}$ of the petrol price. Missing this nuance will lead to the wrong mixture cost. ### Final Answer Therefore, the correct answer is **₹ 2**.