Labour cost is 20% of the cost of production and raw material cost is 10% of the cost of production. The selling price is 20% above the cost of production. If labour cost increases by 40% and raw material cost increases by 20%, while other expenses remain constant and the industry increases the selling price by 10%, what is the new profit percentage?

Introduction / Context:
This question involves cost structure analysis where different components of total cost change by different percentages. Labour and raw materials are specified as percentages of the original cost of production, and then both are increased. The selling price is also changed. We must recompute the total cost and the new selling price, then calculate the resulting profit percentage. This kind of question is common in business math and managerial aptitude tests.

Given Data / Assumptions:

• Original total cost of production = C (assumed).
• Original labour cost = 20% of C = 0.2C.
• Original raw material cost = 10% of C = 0.1C.
• Other expenses = 70% of C = 0.7C.
• Original selling price SP₁ = 20% above cost = 1.2C.
• Labour cost increases by 40% and raw material cost by 20%.
• Other expenses remain at 0.7C.
• New selling price SP₂ is 10% higher than SP₁.

Concept / Approach:
We first compute the new cost components after the increases. The new labour cost becomes 1.4 times the old labour cost, and the new raw material cost becomes 1.2 times the old raw material cost. Adding these to the unchanged other expenses gives a new total cost. The selling price is raised by 10% over the original selling price. Finally, profit% is computed as (SP₂ - new cost) / new cost * 100. Because we use C as a symbolic base, we do not need its actual numeric value.

Step-by-Step Solution:
Step 1: Original cost C is broken down as: labour = 0.2C, raw material = 0.1C, others = 0.7C.Step 2: Original selling price SP₁ = 1.2C.Step 3: Labour cost increases by 40%, so new labour cost = 0.2C * 1.4 = 0.28C.Step 4: Raw material cost increases by 20%, so new raw material cost = 0.1C * 1.2 = 0.12C.Step 5: Other expenses remain unchanged at 0.7C.Step 6: New total cost C₂ = 0.28C + 0.12C + 0.7C = 1.1C.Step 7: Selling price is increased by 10% over SP₁, so SP₂ = 1.1 * SP₁ = 1.1 * 1.2C = 1.32C.Step 8: New profit = SP₂ - C₂ = 1.32C - 1.1C = 0.22C.Step 9: New profit percentage = (0.22C / 1.1C) * 100 = 0.2 * 100 = 20%.

Verification / Alternative check:
Take a simple numerical value, such as C = 100. Then original costs are labour = 20, raw = 10, others = 70, SP₁ = 120. After the changes, new labour cost = 28, new raw cost = 12, others = 70, so new total cost C₂ = 110. New selling price SP₂ = 1.1 * 120 = 132. Profit = 132 - 110 = 22, and profit% = (22 / 110) * 100 = 20%. This numeric example confirms our symbolic result.

Why Other Options Are Wrong:
Profit percentages like 18%, 22% or 24% arise if one incorrectly adjusts only some components of cost or wrongly applies the 10% increase directly to cost instead of selling price. The only value that properly balances the increased cost elements with the higher selling price is 20%.

Common Pitfalls:
Some common mistakes include adding percentage increases directly (for example, adding 40% and 20% and 10%) without considering their different bases, or misinterpreting “20% of cost of production” for labour and raw material share. Another error is to recompute selling price as 20% plus 10% above cost instead of 10% above the old selling price. Keeping careful track of which percentage applies to which base is essential in multi-step cost structure questions.

Final Answer:
After all changes, the new profit percentage for the industry is 20%.