An oil refinery buys crude oil at Rs. 3600 per barrel. During processing there is a 10% wastage. If the refinery wants to earn a 5% profit on its effective cost, then at what price per barrel should it sell the oil so that the selling price includes 8% tax on the selling price?

Introduction / Context:
This question combines several commercial arithmetic ideas: wastage in quantity, desired profit percentage, and tax on the selling price. Such problems are very common in business mathematics and aptitude tests because they require careful step-by-step reasoning and accurate percentage calculations.

Given Data / Assumptions:

Cost price of crude oil for the refinery = Rs. 3600 per barrel purchased.
There is 10% wastage in processing, so only 90% of the purchased oil is actually saleable.
The refinery wants to earn a 5% profit on its effective cost per saleable barrel.
An 8% tax is charged on the selling price, and the final quoted price must include this tax.
We need to find the final selling price per barrel including tax.

Concept / Approach:
Because of the 10% wastage, one barrel purchased does not correspond to one barrel sold. For every barrel sold, more crude must be bought. First we compute the effective cost per saleable barrel by dividing the purchase cost by 0.9. Then we add 5% profit to get the base selling price before tax. Finally, we add 8% tax on this base price to get the final price that the customer pays. Each adjustment must be done multiplicatively and in the correct order.

Step-by-Step Solution:
Step 1: Compute effective cost per saleable barrel. Saleable quantity is 90% of purchased quantity, so cost per saleable barrel = 3600 / 0.9 = Rs. 4000. Step 2: Add 5% profit on this effective cost. Base selling price before tax = 4000 * 1.05 = Rs. 4200. Step 3: Add 8% tax on the selling price. Final selling price including tax = 4200 * 1.08 = 4536. So the refinery should charge Rs. 4536 per barrel (inclusive of tax).

Verification / Alternative Check:
We can check profits: effective cost per saleable barrel is Rs. 4000 and base selling price before tax is Rs. 4200. Profit per barrel before tax = 4200 - 4000 = 200, which is 200 / 4000 = 5%, as required. The tax of 8% on 4200 is 336, and 4200 + 336 = 4536, confirming that the final price correctly includes tax at the right rate.

Why Other Options Are Wrong:
Rs. 3674 and Rs. 3711 are too low; they do not even recover a proper 5% profit on the effective cost once wastage is considered.
Rs. 4219 is closer but effectively ignores or miscalculates the combined effect of wastage, profit, and tax, and does not match the correct multiplicative sequence 3600 → 4000 → 4200 → 4536.

Common Pitfalls:
One common mistake is to take a 5% profit on the original cost of Rs. 3600 without accounting for wastage, which underestimates the needed selling price. Another error is to treat tax as part of profit or to incorrectly apply percentages additively (for example, adding 5% and 8% directly) instead of multiplying step by step. Keeping a clear order—first adjust for wastage, then add profit, then add tax—prevents these errors.

Final Answer:
The refinery should sell the processed oil at Rs. 4536 per barrel including 8% tax.