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# Hasan buys two kinds of cloth materials for school uniforms, shirt material 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 total sale is $ Rs. 36,600 $. How much trouser material did he buy?

Given:

Hasan buys two kinds of cloth materials for school uniforms, shirt material 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 total sale is \( Rs. 36,600 \).

To do:

We have to find the length of the trouser material bought.

Solution:

Let the length of the shirt material bought by Hasan be $3x\ m$.

This implies,

The length of the trouser material bought by Hasan $=2x\ m$.

Cost price of shirt material per metre $=Rs.\ 50$

Selling price of shirt material per metre $= Rs.\ (50 + \frac{12}{100}\times50)$

$= Rs.\ (50+6)$

$=Rs.\ 56$

Cost price of trouser material per metre $=Rs.\ 90$

Selling price of trouser material per metre $= Rs.\ (90 + \frac{10}{100}\times90)$

$= Rs.\ (90+9)$

$=Rs.\ 99$

Total sale $= Rs.\ 36,600$

According to the question,

$(3x \times 56) + (2x \times 99) = 36600$

$168x + 198x = 36600$

$366x = 36600$

$x = \frac{36600}{366}$

$x = 100$

The total trouser material he bought $= 2x$

$= 2 \times 100\ m$

$= 200\ m$

**Hence, Hasan bought $200\ m$ of trouser material.**

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