Question

14. A man buys an article for rs 75. At what price should he sell it to make a profit of 8%? It be sells it for rs 72, what will be his profit or loss per cent?​

Answer 1

Step-by-step explanation:

profit%=profit/CP *100

8=x/75*100

8=4x/3

x=6

selling price=75+6=81

b)

loss=75-72=3

loss%=3/75 *100

=4%

Answer 2

Answer:

The man should sell the article at Rs. 81 to make the required profit.

The loss in the transaction is 4 %.

Step-by-step-explanation:

We have given the cost price and profit percent of an article.

We have to find the selling price of the article.

Let the selling price of the article be Rs. x.

Cost price ( CP ) = Rs. 75

Profit % = 8

Selling price ( SP ) = Rs. x

Now, we know that,

$\displaystyle{\pink{\sf\:Profit\:\%\:=\:\dfrac{Profit}{Cost\:price}\:\times\:100}\sf\:\quad\:-\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:8\:=\:\dfrac{S\:P\:-\:C\:P}{C\:P}\:\times\:100\:\quad\:-\:-\:-\:[\:\because\:Profit\:=\:Selling\ price\ -\ Cost\ price\:]}$

$\displaystyle{\implies\sf\:8\:=\:\dfrac{x\:-\:75}{75}\:\times\:100}$

$\displaystyle{\implies\sf\:8\:=\:\dfrac{(\:x\:-\:75\:)\:\times\:100}{75}}$

$\displaystyle{\implies\sf\:8\:\times\:75\:=\:100\:x\:-\:7500}$

$\displaystyle{\implies\sf\:(\:8\:\times\:75\:)\:+\:7500\:=\:100\:x}$

$\displaystyle{\implies\sf\:\dfrac{(\:8\:\times\:75\:)\:+\:7500}{100}\:=\:x}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{\cancel{75}\:(\:8\:+\:100\:)}{\cancel{100}}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:(\:8\:+\:100\:)}{4}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:\times\:\cancel{4}\:(\:2\:+\:25\:)}{\cancel{4}}}$

$\displaystyle{\implies\sf\:x\:=\:3\:\times\:(\:2\:+\:25\:)}$

$\displaystyle{\implies\sf\:x\:=\:6\:+\:75}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:Rs\:81}}}}$

∴ The man should sell the article at Rs. 81 to make the required profit.

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Now,

We have given that,

Selling price ( SP ) = Rs. 72

Cost price ( CP ) = Rs. 75

We have to find profit or loss per cent.

Here,

CP = 75 > SP = 72

∴ There is loss in the transaction.

Now, we know that,

$\displaystyle{\pink{\sf\:Loss\:\%\:=\:\dfrac{Loss}{Cost\:price}\:\times\:100}\sf\:\quad\:-\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:Loss\:\%\:=\:\dfrac{C\:P\:-\:S\:-\:P}{C\:P}\:\times\:100\:\quad\:-\:-\:-\:[\:\because\:Loss\:=\:Cost\:price\:-\:Selling\:price\:]}$

$\displaystyle{\implies\sf\:Loss\:\%\:=\:\dfrac{75\:-\:72}{75}\:\times\:100}$

$\displaystyle{\implies\sf\:Loss\:\%\:=\:\dfrac{3}{\cancel{75}}\:\times\:\cancel{100}}$

$\displaystyle{\implies\sf\:Loss\:\%\:=\:\cancel{\dfrac{3}{3}}\:\times\:4}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:Loss\:\%\:=\:4}}}}$

∴ The loss in the transaction is 4 %.