Ravi purchases 90 pens and sells 40 pens at a | vedclass

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Question

(A) Let the $CP$ of each pen be $Rs. 100$.At a profit of $10 \%$,the $SP$ of $40$ pens $= (100 + 10) 	imes 40 = Rs. 4400$.At a profit of $20 \%$,the

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$80$

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(A) Let the $CP$ of each pen be $Rs. 100$.At a profit of $10 \%$,the $SP$ of $40$ pens $= (100 + 10) 	imes 40 = Rs. 4400$.At a profit of $20 \%$,the $SP$ of $50$ pens $= (100 + 20) 	imes 50 = Rs. 6000$.Total $SP$ of $90$ pens $= Rs. (4400 + 6000) = Rs. 10400$.Total $CP$ of $90$ pens $= Rs. (90 	imes 100) = Rs. 9000$.If sold at a uniform profit of $15 \%$,the $SP$ of $90$ pens $= Rs. (90 	imes 115) = Rs. 10350$.Difference in $SP = Rs. (10400 - 10350) = Rs. 50$.If the difference is $Rs. 50$,the assumed $CP$ of each pen is $Rs. 100$.If the difference is $Rs. 40$,the actual $CP$ of each pen $= \frac{100 	imes 40}{50} = Rs. 80$.Hence,the cost price of each pen is $Rs. 80$.

Ravi purchases $90$ pens and sells $40$ pens at a gain of $10 \%$ and $50$ pens at a gain of $20 \%$. Had he sold all of them at a uniform profit of $15 \%$,he would have got $Rs. 40$ less. Find the cost price of each pen in $Rs$.

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