# Hasan buys 2 kinds of cloth material for school uniform, shirt material that costs him Rs. 50 per meter and trouser material that costs him 90 per meter. For every 2 meters of trouser material he buys 3 meters of shirt material. He sells the material at 12% and 10% profit respectively. His total sale is Rs. 36660. How much trouser material did he buy?

Last updated date: 25th Mar 2023

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Hint: We need to have a basic idea of cost price, selling price, profit and loss percentages to solve the given problem.

Complete step-by-step answer:

For every 2 meters of trouser, he bought 3 meters of shirt material. We can say that trouser and shirt material lengths are in 2:3 ratio.

Let’s assume Hasan bought 2x meters of trouser material and 3x meters of shirt material.

Selling price = Cost price + Profit

It is given that Hasan sells trouser material at 12% profit.

$ \Rightarrow $ The selling price of trouser material per meter is $ = Rs.90 + \dfrac{{90 \times 12}}{{100}} = 90 + 10.8$

The selling price of trouser material per meter = Rs. 100.80

$\therefore $The selling price of 2x meter trouser material = Rs. $100.8 \times 2x = 201.6x$

It is given that Hasan sells trouser material at 10% profit.

$ \Rightarrow $ The selling price of the shirt material per meter is = $ = Rs.50 + \dfrac{{50 \times 10}}{{100}} = 50 + 5$

The selling price of shirt material per meter = Rs. 55

$\therefore $ The selling price of 3x meter shirt material = $55 \times 3x = 165x$

From the given information, the total amount of sales = Rs. 36660

We have total 5x meter material (2x meters trouser material and 3x shirt material),

Selling price of trouser material + Selling price of shirt material = total amount of sales.

$ \Rightarrow (201.6x) + (165x) = 36660$

$ \Rightarrow 366.60x = 36660$

$ \Rightarrow x = 100$

$\therefore $ Trouser material = 2x = 2(100) =200 meters

Note: Selling price = Cost price + Profit

Selling price is defined as the price at which a good or service is sold by seller to buyer. Cost price is the price at which the article purchased. If we sell the article more than its cost price we will get profit.

Profit = $profit\% \times \cos t\;price.$

Complete step-by-step answer:

For every 2 meters of trouser, he bought 3 meters of shirt material. We can say that trouser and shirt material lengths are in 2:3 ratio.

Let’s assume Hasan bought 2x meters of trouser material and 3x meters of shirt material.

Selling price = Cost price + Profit

It is given that Hasan sells trouser material at 12% profit.

$ \Rightarrow $ The selling price of trouser material per meter is $ = Rs.90 + \dfrac{{90 \times 12}}{{100}} = 90 + 10.8$

The selling price of trouser material per meter = Rs. 100.80

$\therefore $The selling price of 2x meter trouser material = Rs. $100.8 \times 2x = 201.6x$

It is given that Hasan sells trouser material at 10% profit.

$ \Rightarrow $ The selling price of the shirt material per meter is = $ = Rs.50 + \dfrac{{50 \times 10}}{{100}} = 50 + 5$

The selling price of shirt material per meter = Rs. 55

$\therefore $ The selling price of 3x meter shirt material = $55 \times 3x = 165x$

From the given information, the total amount of sales = Rs. 36660

We have total 5x meter material (2x meters trouser material and 3x shirt material),

Selling price of trouser material + Selling price of shirt material = total amount of sales.

$ \Rightarrow (201.6x) + (165x) = 36660$

$ \Rightarrow 366.60x = 36660$

$ \Rightarrow x = 100$

$\therefore $ Trouser material = 2x = 2(100) =200 meters

Note: Selling price = Cost price + Profit

Selling price is defined as the price at which a good or service is sold by seller to buyer. Cost price is the price at which the article purchased. If we sell the article more than its cost price we will get profit.

Profit = $profit\% \times \cos t\;price.$

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