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

According to the question, Trouser material and shirt material are purchased in the ratio of 2:3 by Hasan.

Let 2x m of trouser material and 3x m of shirt material be purchased by him.

Given that,

Cost price of the shirt per meter = ₹50 and Profit % = 12%

Cost price of the trouser per meter = ₹90 and Profit % = 10%

We know that,

Selling price = Cost Price + Profit

where, Profit = Profit% × Cost Price

Thus, per meter selling price of trouser material

= ₹ [90 + (90 × 10/100)]

= ₹99

Per meter selling price of shirt material

= ₹ [50 + (50 × 12/100)]

= ₹56

Since the total sales made is ₹36,600, we get

The total selling price of trousers + Total selling price of shirt = 36600

99 × (2x) + 56 × (3x) = 36600 [Since the number of trousers and shirts are 2x and 3x respectively]

198x + 168x = 36600

366x = 36600

x = 100

Thus, trouser material = 2x m

= (2 × 100) m

= 200 m

Therefore, the trouser material that Hasan bought was 200 m.