Question

a shopkeeper sells 2 articles at rs. 1000 each making a profit of 20% on the first article and get a loss of 20% on the second article. find the net profit or loss he makes​

Answer 1

Answer: SP of article 1 = Rs. 1000

Profit % = 20%

CP of article 1 = SP×100/(100+P%)

= 1000×100/(100+20)

= 100000/120

= Rs. 833.33

SP of article 2 = Rs. 1000

Loss % = 20 %

CP of article 2 = SP×100/(100-L%)

= 1000×100/(100-20)

= 100000/80

= Rs. 1250

Total CP = Rs. 833.33 + Rs. 1250

= Rs. 2083.33

Total SP = Rs. 1000 + Rs. 1000

= Rs. 2000

Here, CP is greater than SP

Loss = CP - SP

= Rs. 2083.33 - Rs. 2000

= Rs. 83.33

Net Loss = Rs. 83.33

Loss % = Loss/CP × 100

= 83.33/2083.33× 100

= 3.99 % approx.

Answer 2

Answer:

$\underline{ \bf{\dag}\:\:\large{\textit{Case 1 :}}}$

$:\implies\sf SP=CP \times (100+Profit)\%\\\\\\:\implies\sf 1000=CP \times (100+20)\%\\\\\\:\implies\sf 1000=CP \times 120\%\\\\\\:\implies\sf 1000=CP \times \dfrac{120}{100}\\\\\\:\implies\sf 1000=CP \times \dfrac{6}{5}\\\\\\:\implies\sf 1000 \times \dfrac{5}{6}=CP\\\\\\:\implies\sf 500 \times \dfrac{5}{3}=CP\\\\\\:\implies\sf CP=\dfrac{2500}{3}$

$\rule{110}{0.8}$

$\underline{ \bf{\dag}\:\:\large{\textit{Case 2 :}}}$

$:\implies\sf SP=CP \times (100-Loss)\%\\\\\\:\implies\sf 1000=CP \times (100-20)\%\\\\\\:\implies\sf 1000=CP \times 80\%\\\\\\:\implies\sf 1000=CP \times \dfrac{80}{100}\\\\\\:\implies\sf 1000=CP \times \dfrac{4}{5}\\\\\\:\implies\sf 1000 \times \dfrac{5}{4}=CP\\\\\\:\implies\sf 250 \times 5=CP\\\\\\:\implies\sf CP=1250$

$\rule{150}{1.5}$

$\underline{\bigstar\:\textsf{Net Loss incurred by shopkeeper :}}$

$\dashrightarrow\sf\:\:Loss\%=\dfrac{Total\:Loss}{CP} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{CP-SP}{CP} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{\left(\dfrac{2500}{3}+1250\right)-\bigg(1000+1000\bigg)}{\left(\dfrac{2500}{3}+1250\right)} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{\left(\dfrac{2500 + 3750}{3}\right)-2000}{\left(\dfrac{2500 + 3750}{3}\right)} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{\dfrac{6250 - 6000}{3}}{\dfrac{6250}{3}} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%= \dfrac{250}{6250} \times 100\\\\\\\dashrightarrow\sf\:\:Loss\%= \dfrac{1}{25} \times 100\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Loss\%=4\%}}$

⠀

$\therefore\:\underline{\textsf{Shopkeeper will incur \textbf{4\% loss} on the articles}}.$

$\rule{200}{2}$

⠀⠀⠀⠀⠀⠀Shortcut Trick

• whenever the Profit% and Loss% are same, & SP are same for both.
• Then there will must Loss%.
• we will just Square the given percentage and divide it by 100.

$\underline{\bigstar\:\textsf{Net Loss incurred by shopkeeper :}}$

$\dashrightarrow\sf\:\:Loss\%=\dfrac{(Loss\%)^2}{100}\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{(20)^2}{100}\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{20\times20}{100}\\\\\\\dashrightarrow\sf\:\:Loss\%=\dfrac{400}{100}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Loss\%=4\%}}$

⠀

$\therefore\:\underline{\textsf{Shopkeeper will incur \textbf{4\% loss} on the articles}}.$