c) A man purchased 10 pens. He sold 5 pens at 25% profit and the remainings
pens at 16% loss. If he received Rs 625 in total, find the cost price of each pen.
(please solve this step by step)
Answers
Let CP= total cost price and SP is the selling price.
For 5 pens at 25% profit, SP=1.25CP
For the remaining 5 pens, sold at 50 each, at a loss of 3%, SP=5x50=250. It is found out that the cost price of this remaining 5 pens is different from the other 5 pens sold at 25% profit.
SP at 25% profit +SP at 3% profit loss=625
1.25CP+ 250 =625
1.25CP=625–250= 375
CP= 375/1.25=300
1.25(300)+ 250=625
375+250=625
Therefore, for 5 pens sold at 25% profit, the Selling Price is Rs 375 and the Cost Price is Rs 300. The Cost Price per pen=300/5= Rs 60 each and Selling Price per pen is Rs 75 each.
For the remaining 5 pens, Selling Price is Rs 50 ea. If the selling price is Rs 50 each and the CP with 3% loss is : SP= 0.97CP=5(50)=250; CP=250/0.97=Rs 257.732. CP per pen=257.732/5= Rs 51.55 per pen
SP at 25% Profit =1.25CP=1.25(300)=Rs 375
SP at 3% loss = Rs 250
Total SP=Rs 375 + Rs 250=Rs 625
Total CP= Rs300+Rs 257.732=Rs 557.732
CP per pen =557.732/10= Rs 55.77 each