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# Hasan buys two kinds of cloth material for school uniforms, shirt material that costs hom Rs 50 per meter and trouser material that costs him Rs 90 per meter. For every 3 meters of shirt material he buys 2 meters of the trouser material. He sells the material at 12% and 10% profit respectively. His total sale is Rs 36,600. How much trouser material did he buy?  Hint: To solve the question, we have to understand the statements given to find the relation between the quantity of shirt and trouser material brought to ease the procedure of solving to find one unknown value instead of two unknown values.

The given cost of one meter of shirt material = 50.
The given cost of one meter of trouser material = 90.
Hasan buys every 3 meters of shirt material when he buys 2 meters of the trouser material. This implies that the ratio of shirt and trouser material bought by Hasan is equal to 3:2.
Let the shirt material bought by Hasan is equal to 3x.
Let the trouser material bought by Hasan is equal to 2x.
Hasan sold the shirt material at a profit of 12%.
We know that the formula for Selling Price is equal to $\left( 1+\dfrac{\operatorname{P}%}{100} \right)\times CP$
Where P% and CP represent the profit and the cost price of the commodity.
By substituting the given values in the above mentioned formula, we get
The selling price of shirt material $=\left( 1+\dfrac{12}{100} \right)\times 50$
$=\left( \dfrac{100+12}{100} \right)\times 50$
$=\left( \dfrac{112}{100} \right)\times 50$
$=\dfrac{112}{2}$
= 56 rupees per meter.
Thus, the total selling price of shirt material $=56\times 3x=168x$rupees.
Hasan sold the trouser material at a profit of 10% .
The selling price of trouser material $=\left( 1+\dfrac{10}{100} \right)\times 90$
$=\left( \dfrac{100+10}{100} \right)\times 90$
$=\left( \dfrac{110}{100} \right)\times 90$
$=11\times 9$
= 99 rupees per meter.
The total selling price of trouser material $=99\times 2x=198x$rupees.
The total sale of the materials $=168x+198x=366x$
But the total sale given is equal to Rs. 36,600
$\Rightarrow 366x=36,600$
$x=\dfrac{36,600}{366}$
$\therefore x=100$
Hasan bought trouser material $=2x=2\times 100=200$meters.

Note: The possibility of mistake is not able to analyse the given information to draw the conclusion that the ratio of shirt and trouser material is 3:2. The other possibility of mistake can be calculations as the values are increased and then calculated.
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