Question

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.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 ` 36,600.How much trouser material did he buy ?

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Answer 1

Appropriate Question :-

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. 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 ₹ 36,600. How much trouser material did he buy ?

$\large\underline{\sf{Solution-}}$

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

So, Let assume that

• Material bought for trouser be 2x metre.

• Material bought for shirt be 3x metre.

So, we have

• Cost Price of 2x metre of trouser material = 90 × 2x = ₹ 180x

• Cost Price of 3x metre of shirt material = 50 × 3x = ₹ 150x

As it is given that, he sells the shirt materials at 12% and trouser material at 10% profit respectively and total sale is ₹ 36600.

We know,

$\boxed{ \rm{ \:Selling \: Price = \frac{(100 + Profit\%) \times Cost \: Price}{100} \: }}$

So, using this, we get

$\rm \: \dfrac{(100 + 12) \times 150x}{100} + \dfrac{(100 + 10) \times 180x}{100} = 36600$

$\rm \: \dfrac{112 \times 3x}{2} + \dfrac{110 \times 9x}{5} = 36600$

$\rm \: 168x + 198x = 36600$

$\rm \: 366x = 36600$

$\rm\implies \:\boxed{ \rm{ \:x \: = \: 100 \: \: }}$

So,

Trouser material bought = 2x = 200 metre.

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Q. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him 50 per meter and trouser material that costs him 90 per meter. For every 3 meters of the shirt material he buys 2 meters of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is 36,600. How much trouser material did he buy ?

Answer:  the trouser material that Hasan bought was 200 m

Explanation: According to the question, Trouser material and shirt material are purchased in the ratio of 2:3 by Hasan.

Let 2x m of trouser material and 3x m of shirt material be purchased by him.

Given that,

Cost price of the shirt per metre = ₹50 and Profit % = 12%

Cost price of the trouser per metre = ₹90 and Profit % = 10%

We know that,

Selling price = Cost Price + Profit

where, Profit = Profit% × Cost Price

Thus, per metre selling price of trouser material

= ₹ [90 + (90 × 10/100)]

= ₹99

Per metre selling price of shirt material

= ₹ [50 + (50 × 12/100)]

= ₹56

Since the total sales made is ₹36,660, we get

Total selling price of trousers + Total selling price of shirt = 36660

99 × (2x) + 56 × (3x) = 36660 [Since the number of trousers and shirts are 2x and 3x respectively]

198x + 168x = 36660

366x = 36660

x = 100 (approx.)

Thus, trouser material = 2x m

= (2 × 100) m

= 200 m

Therefore, the trouser material that Hasan bought was 200 m