Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ` 50 per metre and trouser material that costs him ` 90 per metre.32

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

Shubh,

 

Let us assume that Hasan bought x meters of trouser material

so the shirt material Hasan bought is 3/2x = 1.5x

Cost of the trouser material is 90x and cost of shirt material is 50*1.5 x = 75x

He sells shirt material at a profit of 12%. So sales price is (12+100)*75x/100 = 84x

He sells trouser material for a profit of 10% so sales price is (10+100)*90x/100 = 99x

Now total sale is 36,600

99x + 84x = 36,600

183x = 36600

x = 200

He bought 200 m of trouser material

Answer 2

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 3/2 x or 1.5 x.

 

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 1.5 x meters of shirt material and sold it at RS 56 per meter.  So his total sales of shirt material is 1.5 x * 56 = 84 x.

 

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 * 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!

 

Notice that we never needed to know how much of each material was in each item, or how many items he sold.  The problem could be worked out just by looking at the amount material itself.