question_answer

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 metres of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10%, respectively. His total sale is Rs. 36,600. How much trouser material did he buy?

Answer:

Let shirt material be 3x and trouser material be 2x metres.

The cost of shirt material \[=\text{ }50\times 3x=150x\]

The selling price at 12% profit \[=\text{ }\frac{100+12}{100}\text{ }\times 150\,x\]

\[=\frac{112}{100}\times 150x\]

= 168 x

The cost of trouser. Material \[=90\times 2x=180x\]

The selling price at 10% profit \[=\frac{100+10}{100}\times 180x\]

\[=\frac{110}{100}\times 180x=198x\]

According to question,    168x + 198x = 36,600

or,                              366x = 36,600

or,                                  \[x=\frac{36600}{366}\]

or,                                   x = 100

\[\therefore \]      Trouser material \[=2\times 100=200\text{ }m\]

Hence, Hasan bought 200 m trouser material.