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# 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 2 metres of the trouser material, he buys 3 metres of the shirt material. He sells the shirt material at 12% profit and trouser material at 10% profit. His total sale is Rs 36,600. How much trouser material did he buy?A. 70mB. 150mC. 120mD. 200m

Last updated date: 22nd Mar 2023
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Hint:- Here we use the formula of profit. If an item costs Rs x and shopkeeper sells it at profit of y% then selling price of that item will be x + $\dfrac{{\text{y}}}{{{\text{100}}}}{\text{*x}}$ = Rs x*$\left( {\dfrac{{{\text{100 + y}}}}{{{\text{100}}}}} \right)$.

As it is given in question that cost of trouser per metre is Rs 90.
And profit on trouser per metre is 10%.
So, cost of trouser per metre including profit will be Rs 90*$\left( {\dfrac{{{\text{100 + 10}}}}{{{\text{100}}}}} \right)$ = Rs 90*1.1 = Rs 99.
As it is given in the question that the cost of a shirt per metre is Rs 50.
And profit on shirt per metre is 12%.
So, cost of shirt per metre including profit will be Rs 50*$\left( {\dfrac{{{\text{100 + 12}}}}{{{\text{100}}}}} \right)$ = Rs 50*1.12 = Rs 56.
As it is given in the question that Hasan buys 3 metres of shirt for every 2 metres of trouser.
So, cost of each pair including profit will be Rs (3*56 + 2*99) = Rs 366.
And it is given that Hasan total sale is Rs 36600.
So, the number of pairs Hasan has sold will be equal to the total sale divided by the selling cost of one pair.
So, total pairs Hasan had sold = $\dfrac{{{\text{36600}}}}{{{\text{366}}}}$ = 100.
As we know that in one pair there are 2 metres of trousers and 3 metres of shirt.
So, the length of trouser material Hasan had bought will be equal to two times the number of pairs Hasan had sold.
So, length of trouser material Hasan had brought will be 2*100 metres = 200 metres.
Hence, the correct option will be D.
Note:- Whenever we come up with this type of problem then first, we find the total profit on each pair of cloth. And then after that we will find the selling price of cloth for each pair. After that we can divide the total sale price with the selling price of one pair to get the number of pairs sold. After that we can easily get the length of trouser by multiplying the number of pairs with the length of trouser in one pair.