The concentration of petrol in three different mixtures of petrol and kerosene is 1/2, 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three mixtures and combined, what is the ratio of petrol to kerosene in the resulting mixture?

Introduction / Context:
This question involves mixing solutions with different concentrations and then finding the composition of the resulting mixture. It tests comfort with fractions, weighted averages and the idea that total amount of petrol and kerosene is additive across the mixtures.

Given Data / Assumptions:

• Mixture 1: petrol fraction = 1/2, kerosene fraction = 1/2, volume taken = 2 litres.
• Mixture 2: petrol fraction = 3/5, kerosene fraction = 2/5, volume taken = 3 litres.
• Mixture 3: petrol fraction = 4/5, kerosene fraction = 1/5, volume taken = 1 litre.
• We must find petrol : kerosene in the combined mixture.

Concept / Approach:
We calculate the quantity of petrol and kerosene from each mixture separately using the relation quantity = fraction * total volume. Then we add petrol amounts together and kerosene amounts together. The ratio of these totals gives the composition in the final mixture. This is a straightforward application of mixture and alligation concepts.

Step-by-Step Solution:
Step 1: From mixture 1 (2 litres, petrol 1/2), petrol quantity = 2 * 1/2 = 1 litre and kerosene quantity = 2 * 1/2 = 1 litre. Step 2: From mixture 2 (3 litres, petrol 3/5), petrol quantity = 3 * 3/5 = 9/5 litres = 1.8 litres and kerosene quantity = 3 * 2/5 = 6/5 litres = 1.2 litres. Step 3: From mixture 3 (1 litre, petrol 4/5), petrol quantity = 1 * 4/5 = 0.8 litres and kerosene quantity = 1 * 1/5 = 0.2 litres. Step 4: Total petrol = 1 + 1.8 + 0.8 = 3.6 litres. Step 5: Total kerosene = 1 + 1.2 + 0.2 = 2.4 litres. Step 6: Petrol : kerosene in final mixture = 3.6 : 2.4. Step 7: Divide both sides by 1.2 to simplify: 3.6 ÷ 1.2 = 3 and 2.4 ÷ 1.2 = 2. Step 8: So the ratio becomes 3 : 2.

Verification / Alternative check:
Total mixture volume is 2 + 3 + 1 = 6 litres. Petrol fraction in final mixture is 3.6 / 6 = 0.6, kerosene fraction is 2.4 / 6 = 0.4. The ratio 0.6 : 0.4 simplifies to 6 : 4 which further simplifies to 3 : 2. This confirms that the ratio 3 : 2 is consistent.

Why Other Options Are Wrong:
Ratios such as 4 : 5, 3 : 5 or 2 : 3 represent either an overall lower or higher petrol fraction, which does not match the computed 60% petrol and 40% kerosene. For example, 2 : 3 would correspond to 40% petrol and 60% kerosene, which contradicts our calculations.

Common Pitfalls:
One common mistake is to average the fractions directly as (1/2 + 3/5 + 4/5) / 3 without weighting by volumes, which is wrong. Another error is to add the ratios instead of quantities. Always remember that ratios describe relative amounts but actual computations must be done on absolute quantities obtained by multiplying fractions with volumes.

Final Answer:
The ratio of petrol to kerosene in the resulting mixture is 3 : 2.