11. Hasan buys two kinds of cloth materials for school uniforms, shirt materiald that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at $$ 12 \% $$ and $$ 10 \% $$ profit respectively. His totai sale is Rs 36,600 . How much trouser material did he buy?

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Let's break down the problem step by step to find out how much trouser material Hasan bought.

**Given:**
- **Shirt material cost:** Rs 50 per metre
- **Trouser material cost:** Rs 90 per metre
- **Buying ratio:** For every 3 metres of shirt material, he buys 2 metres of trouser material.
- **Profit on shirts:** 12%
- **Profit on trousers:** 10%
- **Total sales:** Rs 36,600

**Step 1: Determine the Quantities Bought**
Let’s assume Hasan buys:
- **3x metres** of shirt material
- **2x metres** of trouser material

**Step 2: Calculate Selling Prices**
- **Selling price of shirts:** 
  $$
  50 + 0.12 \times 50 = 50 + 6 = Rs 56 \text{ per metre}
  $$
- **Selling price of trousers:** 
  $$
  90 + 0.10 \times 90 = 90 + 9 = Rs 99 \text{ per metre}
  $$

**Step 3: Set Up the Sales Equation**
The total sales from both materials can be expressed as:
$$
\text{Total Sales} = (3x \times 56) + (2x \times 99)
$$
$$
36,600 = 168x + 198x
$$
$$
36,600 = 366x
$$

**Step 4: Solve for $$ x $$**
$$
x = \frac{36,600}{366} = 100
$$

**Step 5: Find the Amount of Trouser Material Bought**
Since Hasan buys **2x** metres of trouser material:
$$
2x = 2 \times 100 = 200 \text{ metres}
$$

**Answer:**  
Hasan bought **200 metres** of trouser material.
Hasan bought 200 metres of trouser material.

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