Profit and Loss IMPORTANT FACTSCost Price:The price, at which an article is purchased, is called itscost price, abbreviated asC.P.Selling Price:The price, at which an article is sold, is called itsselling prices, abbreviated asS.P.Profit or Gain:If S.P. is greater than C.P., the seller is said to have aprofitorgain.Loss:If S.P. is less than C.P., the seller is said to have incurred aloss.Cost Price (C.P),Selling Price ( S.P),Market Price (M.P) or Retail Price (R.P) or List Price, Discount Price .Formulas such as ,1. Profit = S.P C.P :: S.P >C.P2. Loss = C.P S.P :: C.P > S.P3. Profit % = (Profit / C.P )*100 or4. Profit % = {(S.P C.P)/C.P }*1005. Loss % = (Loss / C.P )*100 or6. Loss % = {(C.P S.P)/C.P }*1007. S.P = {(100+Gain % )/100}*C.P or8. C.P = {100 / (100+gain %)}*S.P9. S.P = {(100-Loss % )/100}*C.P or10. C.P = {100 / (100-Loss %)}*S.P11. When a Person sells two similar items, one at a gain of x% and the other at a loss of x%, then the seller always incurs a loss of is :Loss %= {(Common Loss and Gain %)/ 10 }2=(x/10)212. When a Person buys two similar items, sells one at a gain of x% and the other at a loss of x%, then the seller incursno gain no loss13. If a trader profess to sell his goods at cost Price, But uses false weights, thenGain % = {(error)/ ((True Value)-(Error))}*100 %Important Points to remember that : Profit % and Loss % is fully based on Cost Price alone .Profit =10% i.e. 10% of Cost Price is Profit .This is the meaning of 10% Profit. Discount is fully based on the Market Price/Retail Price/List Price.Discount = 10% i.e. 10% on Market Price is Discount .This is the meaning of 10% Discount. Doubling the price and then reducing it by 50% does not yield 50% profit the net effect is no-profit-no-loss. Successive discounts of 10%, 20% and 30% does not yield an overall 60% discount the actual total is only 49.6%. Successive discounts of 25%, 10% and 5% is not the same as successive discounts of 20%, 15% and 5% although both add up to 40%. The actual total discounts are 35.875% and 35.4% respectively. A is 200% of B => A = 2B. But A is 200% more of B = >A = 3B. Similarly, P is twice as old as Q => Ps age = 2 Qs age, but A is twice older than B = >As age = 3 Bs age. If,by selling an article for Rs 100, a man gains Rs 15, then his gain percent is : 15% 12(2/3)% Ans:17(11/17)% 17(1/4)% Soln: S.P. = Rs.. 100 gram = Rs. 15. So, C. P. Rs.(100 - 15) = Rs 85 .: Gain % = [( 15/85) * 100]% = 17(11/17)% 2:Example:1.A man buys an article for Rs.27.50 and sells it for Rs.28.60.Find his gain percent ?Buys denotes the cost price , c.p = 27.50Sells denotes the selling price, s.p = 28.60For finding the profit % by two methods.1. find the profit and apply on (3) profit % formula2. Directly apply in 7 th formula.Decide which is easy for you .First methodProfit = 28.60 27.50 = 1.10Profit % = (1.10 / 27.50)*100 = 4%Second MethodBH. = ((100 + gain% )/100 }27.50(28.60*100 )/27.50 = 100 + gain %Gain % = 104-100 = 4%2.John bought a satellite radio for rs 4,000 and sold it at a loss of 5% due to unavoidable circumstances.Find his Selling Price ?Cost Price = 4000Loss = 5 %From the formula 7 ,we can get it directly ,Selling Price = rs3800.Check with your answer3.If the cost Price of two articles is 1000 each, one of them is sold at 10% profit and the other at 10% loss. Find the percentage of profit or loss on the whole transaction ?From formula 12 ,we can say directly No Loss No Gain .Lets Check out,Total Cost Price = Rs.2000.Need to find the total Selling Price ,By the Formula 7,Selling Price of one article (10% profit) = 1100By the Formula 8,Selling Price of another article (10% loss) = 900So the total selling price = 1100+900 = Rs.2000.Selling Price = Cost Price .So No Loss No Gain in whole transaction.4.If the Selling Price of two articles is 1000 each, sold one at 10% profit and the other at 10% loss. Find the percentage of profit or loss on the whole transaction ?From formula 11, we can say that loss %= (10/10)2=1%Lets check out in another way ,Total Selling Price = Rs.2000By the Formula 7,Cost Price of one article (sold at 10% profit) = 909.09By the Formula 8,Cost Price of another article (sold at 10% loss) = 1111.11Total Cost Price= 909.09+1111.11 =Rs.2020.20here C.P > S.P . So loss incurs in whole transaction.Loss % ={(2020.20 2000 )/ 2020.20 }*100= 1.00%We have verified the answer in both the way. So we can use formula directly5.The selling price of 15 chairs is equals to the cost price of 20 chairs. Find the Profit or Loss % ?Given , S.P of 15 chairs = C.P of 20 chairs.From the above eqn we can conclude that we can get profit. Because Selling 15 chair itself we will get the total cost of the 20 chairs. So we get the profit of selling 5 chairs.First method,Using Profit% formula we can find the answer,Profit% = (Profit/ Cost Price )*100Profit % = {(S.P of 5 chairs)/(S.P of 15 chairs or C.P of 20 chairs) }*100Profit % = (5/15)* 100 = 33.33%Second method,Let we take cost price be Rs 1,selling price be Rs x.from the eqn, we can write 15x = 20 ; x = Rs. 1.3333S.P > C.P , So we will get profit only. Profit = 1.3333 1.00 = Rs. 0.3333Profit %= (0.3333/1 )*100 =33.33%Third method,Let we take cost price be rs x and selling price be rs y