Question

some articles were was marked 25% above their cost price. One of such articles was sold at 20% profit on the marked price and the other one was sold at 10% loss on the marked price .Find the overall percentage profit.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Profit\%=31.25\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Marked \: price = 25\% \: above \: Cost \: price \\ \\ \tt: \implies Profit \% = 20\% \: on \: selling \: an\: article \\ \\ \tt: \implies Loss\% = 10\% \: on \: Selling \: an \: article \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies overall \: Profit\% =?$

• According to given question :

$\circ \: \text{Let \: Cost \: price = 100} \\ \\ \circ \: \tt{Marked \: price = 125} \\ \\ \bold{For \: Profit \: on \: article} \\ \tt: \implies New \: Selling \: price = Marked \: price + Profit\% \\ \\ \tt: \implies New \: Selling \: price =125 + 20\% \: of \: 125 \\ \\ \tt: \implies New \: Selling \: price =125 + 25 \\ \\ \green{\tt: \implies New \: Selling \: price =150} \\ \\ \bold{For \: loss \: on \: article} \\ \tt: \implies New \: Selling \: price = Marked \: price - Loss\% \\ \\ \tt: \implies New \: Selling \: price =125 - 10\% \: of \: 125 \\ \\ \tt: \implies New \: Selling \: price =125 -12.5 \\ \\ \green{\tt: \implies New \: Selling \: price =112.5} \\ \\ \circ \: \text{Total \: Cost \: price \: of \: both \: article = 200} \\ \\ \circ \tt{\:Profit = 150 + 112.5 - 200} \\ \\ \tt \: \: Profit = 62.5 \\ \\ \bold{For \: profit \%} \\ \tt: \implies Profit\% = \frac{Profit}{C.P} \times 100 \\ \\ \tt: \implies Profit\% = \frac{62.5}{200} \times 100 \\ \\ \green{\tt: \implies Profit\% =31.25\%}$

Answer 2

Given :

• Marked price = 25% above Cost price
• Profit% is 20%
• Loss% is 10%

To Find :

• Total / overall Profit %

Let the Cost price be 100, then the Marked price will become 125.

______________________________

For Profit on given articles :

Selling price = Marked price + Profit %

→ S.P = 125 + 20 % of 125

→ S.P = 125 + 25

→ S.P = 150

______________________________

For Loss on given articles :

Selling price = Marked price – Loss %

→ S.P = 125 – 10 % of 125

→ S.P = 125 – 12.5

→ S.P = 112.5

______________________________

Total Cost price of both the articles = 200

Profit = ( 150 + 112.5 ) – 200

→ Profit = 262.5 – 200

→ Profit = 62.5

______________________________

Now, Total Profit % :

$\sf{Profit \% = \dfrac{Profit}{C.P} \times 100} \\ \\ \rightarrow \: \sf{Profit \% = \dfrac{62.5}{200} \times 100} \\ \\ \rightarrow \: \sf{Profit \% = 31.25 \: \%}$

So, the overall profit % is 31.25 %