Question

Hasan buys two kinds of cloth material for school uniforms, shirt material that costs him $Rs.50$ per metre and the trouser material costs him $Rs.90$ per metre. For every $3$ metre of shirt material, he buys 2 metres of the trouser material. He sells the materials at $12\%$ and $10\%$ profit respectively. His total sale is $Rs.36600.$ How much trouser material did he buy?

Answer 1

The cost price of the shirt material $=Rs.50$

The cost price of the trouser material $=Rs.90$

For every 3 metres of shirt material, he buys 2 metres of trousers.

$\frac{\text{Shirt material purchased}}{\text{Trouser material purchased}}=\frac{3}{2}$

Let the shirt material purchased $=3x$ metres

and, the trouser material purchased $=2x$ metres

The total cost of $3x$ metres shirt material $=3x\times 50=Rs.150x$

The selling price of $3x$ metres shirt material @ $12\%$ profit $=$ C.P $+$ Profit

$=150x+12\%$ of $150x=150x(1+\frac{12}{100})=150x\times \frac{112}{100}=Rs.168x$

The total cost of $2x$ metres trouser material $=2x\times 90=Rs.180x$

The selling price (S.P) of $2x$ metres trouser material @ $10\%$ profit $=180x+10\%$ of $180x=180x(1+\frac{10}{100})=180x\times \frac{110}{100}=Rs.198x$

Total Sale is given as $Rs.36600$

$\therefore$ S.P of total shirt material $+$ S.P of total trouser material $=Rs.36600$

$\Rightarrow 168x+198x=36600$

$\Rightarrow 366x=36600$

$\Rightarrow x=100$

So, the total trouser material hasan bought$=2x=2\times 100=200$ metres