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

Step 1: Given data

• Given: the cost of the shirt material $=$Rs.$50$ per metre.
• The cost of the trouser material $=$Rs.$90$ per metre.
• Profit on shirt material$=12\%$and profit on trouser material$=10\%$.
• Total sale is Rs.$36,600$.
• For every $3$ meters of the shirt material he buys $2$ metres of the trouser material

Step 2: Find the selling price of 1 metre of shirt and trouser

The material of the shirt Hasan bought$=3x$

The material of the trouser Hasan bought$=2x$

The selling price of 1 meter of shirt$=50+\left(50\times \frac{12}{100}\right)$

$$\begin{gathered} =50+6 \\ =Rs56 \end{gathered}$$

The selling price of 1 meter of trousers$=90+\left(90\times \frac{10}{100}\right)$

$$\begin{gathered} =90+9 \\ =Rs99 \end{gathered}$$

Step 3: Find the amount of material of trouser

The total amount of sale$=36600$

$$\begin{gathered} \Rightarrow 56\times 3x+99\times 2x=36600 \\ \Rightarrow 168x+198x=36600 \\ \Rightarrow 366x=36600 \\ \Rightarrow x=100 \end{gathered}$$

therefore, amount of trouser material$=2x\Rightarrow 2\times 100$

$=200metres$

Hence, the amount of material for trousers Hasan bought is $200$ metres.