A small and medium enterprise imports two components A and B from Taiwan and China respectively
and assembles them with other components to form a toy. Component A contributes to 10% of production
cost while component B contributes to 20% of production cost. Usually the company sells this toy at 20%
above the production cost. Due to increase in the raw material and labour cost in both the countries,
component A became 20% costlier and component B became 40% costlier. Owing to these reasons the
company increased its selling price by 15%. Considering that cost of other components does not change, what
will be the profit percentage if the toy is sold at the new price

Let's break down the problem step by step to find the profit percentage after the price changes.

### Initial Conditions:

- Let the initial production cost be \( C \).
- Component A contributes 10% of the production cost: \( C_A = 0.1C \).
- Component B contributes 20% of the production cost: \( C_B = 0.2C \).
- Other components contribute \( C_O = C - C_A - C_B = 0.7C \).
- Selling price is initially set at 20% above the production cost: \( S = 1.2C \).

### Price Increase:

- Component A became 20% costlier, so the new cost of A is:
  \[
  C'_A = 1.2 \times 0.1C = 0.12C
  \]
- Component B became 40% costlier, so the new cost of B is:
  \[
  C'_B = 1.4 \times 0.2C = 0.28C
  \]
- Cost of other components remains the same: \( C'_O = 0.7C \).

### New Production Cost:

The new production cost \( C' \) is the sum of the new costs of components A, B, and other components:
\[
C' = C'_A + C'_B + C'_O = 0.12C + 0.28C + 0.7C = 1.1C
\]

### New Selling Price:

The company increased its selling price by 15%, so the new selling price \( S' \) is:
\[
S' = 1.15 \times 1.2C = 1.38C
\]

### Profit Calculation:

The profit is the difference between the selling price and the production cost:
\[
\text{Profit} = S' - C' = 1.38C - 1.1C = 0.28C
\]

### Profit Percentage:

The profit percentage is given by:
\[
\text{Profit Percentage} = \frac{\text{Profit}}{\text{Production Cost}} \times 100 = \frac{0.28C}{1.1C} \times 100 = \frac{0.28}{1.1} \times 100 \approx 25.45\%
\]

### Final Answer:
The profit percentage after the price changes is approximately **25.45%**.

Would you like any additional details or have any questions? Here are some related questions that could be explored:

1. How would the profit percentage change if only one component's cost increased?
2. What would be the new profit percentage if the selling price was not increased?
3. How would the profit percentage differ if the initial selling price markup was different?
4. What if component A's cost increase was 10% instead of 20%?
5. How does the change in profit percentage affect the overall revenue?

**Tip:** Always consider how each component contributes to the overall cost when analyzing the impact of cost changes on profits.

Explore how to calculate the profit percentage after price changes in toy production. Understand the impact of increased costs for components A and B from Taiwan and China, respectively, and how the selling price adjustment affects profitability. Suitable for advanced high school students and beyond.

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