Question

B. A trader sold 1750 articles for Gh52,500.00 and made a profit of 20%
i. calculate the cost price of each article
ii. if he wanted 45%profit on the cost price , how much should he have sold each of the article

Answer 1

I. 30

ii. 43.5

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Answer 2

Solution of i.

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

• Selling Price of 1750 articles = Gh 52500

• Profit % = 20 %

$\large\underline{\sf{To\:Find - }}$

• Cost Price of 1 article.

Basic Concept Used :-

We're given with the selling price and the profit gained by selling an article. And we have to find the cost price of the article. For finding this, first let's recall the chapter- "Profit and Loss", which we've studied in previous classes!

• Cost Price (C.P.) - The price at which an article is purchased is called it's cost price.

• Selling Price (S.P.) - The price at which an article is sold is called it's selling price.

• Profit - If the S.P. of an article is greater than its C.P., we say that there is a profit.

• Loss - If the S.P. of an article is less than its C.P., we say that there is a loss.

• Overheads - All the expenditure incurred on transportation, repairs, etc are categorised as overheads. Overheads are always included in the C.P. of the article.

In this question, we're only going to deal with the first three sub-topics which are mentioned above.

Let's start calculating the required answer!!

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

Selling Price of 1750 articles = Gh 52500

So,

Selling Price of 1 article = 52500 ÷ 1750 = Gh 30.

Profit % = 20 %

We know that,

$\boxed{ \sf \: Cost \: Price = \dfrac{Selling \: Price \times 100}{100 + Profit \: \%} }$

On substituting the values, we get

$\rm :\longmapsto\:Cost \: Price \: = \dfrac{100 \times 30}{100 + 20}$

$\rm :\longmapsto\:Cost \: Price \: = \dfrac{3000}{120}$

$\bf\implies \:Cost \: Price \: = \: Gh \: 25$

$\overbrace{ \underline { \boxed { \rm \therefore \: Cost \: Price \: of \: 1 \: article \: = \: Gh \: 25)}}}$

Solution of ii.

Now, we have,

• Cost Price of 1 article = Gh 25

• Profit % = 45 %

We know that,

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

On substituting, the values we get

$\rm :\longmapsto\:Selling \: Price \: = \dfrac{(100 + 45) \times 25}{100}$

$\rm :\longmapsto\:Selling \: Price \: = \dfrac{145}{4}$

$\rm :\longmapsto\:Selling \: Price \: = Gh \: 36.25$

$\overbrace{ \underline { \boxed { \rm \therefore \: Selling \: Price \: of \: an \: article \: = \: Gh \: 36.25)}}}$

Additional Information :-

$\boxed{ \sf \: Profit = Selling \: Price - Cost \: Price}$

$\boxed{ \sf \: Loss = Cost \: Price - Selling \: Price}$

$\boxed{ \sf \: Cost \: Price = \dfrac{Selling \: Price \times 100}{100 - Loss \: \%} }$

$\boxed{ \sf \: Selling \: Price \: = \: \dfrac{(100 - Loss\%) \times Cost \: Price}{100}}$

$\boxed{ \sf \: Profit\% = \dfrac{Profit}{Cost Price} \times 100\%}$

$\boxed{ \sf \: Loss\% = \dfrac{Loss}{Cost Price} \times 100\%}$