Question

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A shopkeeper gains 20% while buying the goods and 30% while selling them. find his total gain percent .


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Answer 1

AnswEr :

Let the CP of the good be Rs. 100

$\longrightarrow\sf New \:CP = CP \times \dfrac{(100+Gain\%)}{100}\\\\\\\longrightarrow\sf New \:CP = 100\times \dfrac{(100+20)}{100}\\\\\\\longrightarrow\sf New \:CP =(100+20)\\\\\\\longrightarrow\sf New\:CP =120$

$\rule{120}{2}$

$\longrightarrow\sf SP = New \:CP \times \dfrac{(100+Gain\%)}{100}\\\\\\\longrightarrow\sf SP =120 \times \dfrac{(100+30)}{100}\\\\\\\longrightarrow\sf SP =120 \times \dfrac{130}{100}\\\\\\\longrightarrow\sf SP =12 \times 13\\\\\\\longrightarrow\sf SP =156$

$\rule{150}{1}$

• G A I N ⠀P E R C E N T A G E :

$:\implies\sf Gain\%=\dfrac{Gain}{CP} \times 100\\\\\\:\implies\sf Gain\%=\dfrac{(SP-CP)}{CP} \times 100\\\\\\:\implies\sf Gain\%=\dfrac{(156-100)}{100} \times 100\\\\\\:\implies\sf Gain\%=(156-100)\\\\\\:\implies \boxed{\sf Gain\%=56\%}$

⠀

$\underline{\therefore\:\textsf{Total gain percentage of seller is \textbf{56\%}}}$

$\rule{200}{2}$

• S H O R T C U T ⠀T R I C K :

$:\implies\tt Gain\%=(P_1 + P_2) + \dfrac{P_1P_2}{100}\\\\\\:\implies\tt Gain\%=(20+30) + \dfrac{20 \times 30}{100}\\\\\\:\implies\tt Gain\%=50+(2 \times 3)\\\\\\:\implies\tt Gain\%=50+6\\\\\\:\implies \boxed{\tt Gain\%=56\%}$

⠀

$\underline{\therefore\:\textsf{Total gain percentage of seller is \textbf{56\%}}}$

Answer 2

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