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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 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36660. How much trouser material did he buy?

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

cost of shirt material per unit length=50 rs/m cost of trouser material per unit length=90 rs/m For every 2 meters of the trouser material, he buys 3 meters of the shirt material. ie ratio of shirt to trouser material=3:2 profit of shirt material = 12% profit of trouser material=10% total sale =36660 since...
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cost of shirt material per unit length=50 rs/m

cost of trouser material per unit length=90 rs/m

For every 2 meters of the trouser material, he buys 3 meters of the shirt material. 

ie ratio of shirt to trouser material=3:2

profit of shirt material = 12%

profit of trouser material=10%

total sale =36660

since shirt and trouser length he bought are in the ratio 3:2,

length of shirt material he bought=3k

length of trouser material he bought=2k

cost of shirt material=3k*50=150k

cost of trouser material=2k*90=180k

where k is an integer constant.

selling price=cost price(1+profit/100)

selling price of shirt material=150k*(1+12/100)=150k*(1+0.12)=150*1.12*k=168k

selling price of trouser material=180k*(1+10/100)=180k*(1+0.1)=180*1.1*k=198k

total selling price=168k+198k=366k

366k=36660

k=36660/366~100

trouser material he bought=2k=200 m

 

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Let 2x m of trouser material and 3x m of shirt material be bought by him. Per metre selling price of trouser material = = Rs 100.80 Per metre selling price of shirt material = = Rs 55 Given that, total amount of selling = Rs 36660 100.80 × (2x) + 55 × (3x) = 36660 201.60x + 165x = 36660 366.60x...
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Let 2x m of trouser material and 3x m of shirt material be bought by him.

Per metre selling price of trouser material = = Rs 100.80

Per metre selling price of shirt material = = Rs 55

Given that, total amount of selling = Rs 36660

100.80 × (2x) + 55 × (3x) = 36660

201.60x + 165x = 36660

366.60x = 36660

Dividing both sides by 366.60, we obtain

x = 100

Trouser material = 2x m = (2 × 100) m = 200 m

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