Question

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?

Answer 1

Assign a variable to the amount of trouser material, since that's what you're trying to figure out. Call it $x$..

So you know that the amount of shirt material he bought is $\frac{3}{2}x$ or $1.5x$.

The shirt material costs $Rs.50$ per meter, and he sells it at a profit of $12\%$.

That means that his profit per meter is $12\%$ of $50$, which is $6$.

So the sales price associated with each meter of shirt material is $56$.

The trouser material costs $Rs.90$ per meter, and he sells it at a profit of $10\%$.

That means that his profit per meter is $10\%$ of $90$, which is $9$.

So the sales price associated with each meter of shirt material is $99$.

So he bought $1.5x$ meters of shirt material and sold it at $Rs.56$ per meter.

So his total sales of shirt material is $1.5x\times 56=84x$.

And he bought $x$ meters of trouser material and sold it at $Rs.99$ per meter.

So his total sales of trouser material is $x\times 99=99x$.

So his total sales are $84x+99x=183x$.

And we know that his total sales are $Rs.36,600$.

So let $183x$ equal to $36600$ and solve:

$183x=36600$.

$x=200$

Since we defined $x$ to be the amount of trouser material, then that is the answer!