Profit and Loss With solved examples including shortcut methods

Profit and Loss

C.P = Cost price = the price at which an article is purchased. S.P = Sell price = the price at which an article is sold. Formulae: i. Profit or Gain = S.P – C.P ii. Loss = C.P – S.P iii. Profit % = (profit/ CP) × 100 iv. Loss % = (loss/CP) × 100 v. Profit and loss are always counted on CP vi. CP is always 100% in case of profit and loss Observations i. In case of profit or loss, the relation is generated between CP and SP. IF 20% profit occurs on and article, it means 100% represent the cost price 90% represent the selling price 10% represent profit i.e profit 20% C.P 100% % S.P 120% ii. if 10% loss occurred in an article, it means: 100% represents the cost price 90% sell price 10% represent the loss Important points i. When Cost price CP and profit or loss Percentage is given Then CP = SP × (100 + profit) ÷ 100 CP = SP × (100 - Loss%) ÷ 100 ii. When Sell price and profit or loss percentage is given Then SP = CP × 100 ÷ (100 + profit%) SP = CP × 100 ÷ (100 - Loss%) iii. Marked price: MRP of an article is known as marked price or labeled price denoted by MP. Discount The reduction made on marked price is known as a discount i. Discount = MP – SP ii. Discount percentage = Discount ÷ MP × 100 iii. When the Marked price and the discount percentage is given then SP = MP × (100- Discount %) ÷ 100 iv. Relation between CP and MP MP = [CP × (100 ± profit or Loss%)] ÷ (100- discount) + for profit, - For loss Successive Discount i. Discount equivalent to successive discounts of x% and y% of an article (x + y – XY ÷ 100) % ii. Discount equivalent to successive discounts of x%, y%, and z%. P = (x + y – xy ÷ 100) % Equivalent discount of p and z = (p + z – pz ÷ 100) %

Solved examples (open to view)

• Ex.1 A fruit seller makes a profit of 20% by selling mango at a certain price if the change 2Rs.. more for each mango then he can make a profit of 40%. Then find the CP of 1 mango.

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  Sol. Let Cost price of mango is 100 Then, 20% profit means sales price of mango is 120 Now 40% profit means Sales price of mango is 140 Now 2 Rs. more change profit from 120 to 140 This means 2 = 20% 100% = 2 * (100/20) = 10 Rs. Ans.
• Ex.2 A man purchased 2 fans for Rs. 1200 each and he sold one at 10% profit and the other he loses 5% then find the overall profit.

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  Sol. The cost price of fans is = 2400 Rs. 1200 Rs. + 1200 Rs. (1200 * 10/100) - (1200 * 5/100) 120 - 60 = 60 Rs. (60/2400) * 100 = 2.5% Ans. Method 2 If two articles both have same price then (+profit% - loss%)/Number of articles (10% - 5%)/2 = 2.5% Ans
• Ex.3 If the cost price of an article is 1900 Rs. if 5/7 of its part is sold at a profit of 6% and remaining at a loss of 8%. then find its overall profit% or loss%.

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  Sol. If articles are given in terms of part 5/7 The denominator gives the number of articles. thus the total number of articles is 7. 5 articles are sell at 6% profit and 2 articles are sell at 2% loss. (+profit% - loss%)/Number of articles (5*6% - 2*8%)/ 7 = 2% Ans
• Ex.4 If the cost price of an article is 2500 Rs. if 2/3 of it is sold in the profit of 4% then in what % profit he sells the rest part to gain an overall 5% profit.

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  Sol. Let the total number of article is 3. 2 articles are sold at the profit of 4%. and 1 article is at x% (2*4 + x)/3 = 5% Ans
• Ex.5 By selling 32 orange for 30 Rs. A man losses 25% to gain 20% profit find the selling price of 4 orange.

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  Sol. 32 Orange = 30 Rs. 1 Orange = 30/32 Rs 4 Orange = (30/32) * 4 = 15/4 S.P % S.P 75% 15/4 120% = (15/4) * (120/75) 75% = 15/4 1% = (15/4) *1/75 120% = (15/4)*120/75 = 6 Rs. Ans
• Ex 6 A man sold 2 articles at the same price on first he gains 25% and the other he loses 20% then find it is his overall profit or loss percent.

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  Sol. If S.P is the same. Method 1. 25% = 1/4 (equivalent fraction) 20% = 1/5 In this case, 4 is cost price. in case of profit we add 1 with denominator to find S.P which is 5 In case of loss, we subtract 1 with the denominator. in the case of 20%, C.P is 5 and S.P is 4 Now we have to make a sale price equal. multiply the equation by 4 and 5 C.P= 41 S.P = 40 loss =1 (1/41)*100 = 100/41 Method 2 CP1/CP2 = 16/25 CP = 16+25= 41 Profit or loss = 16* (25/100) - 25 *(20/100) = -1 Loss = (1/41) * 100 = 100/41 Method 3 Formula = [100(P-L)- 2*P*L]/(100+P)+(100-L) [100(25-20)- 2*25*20]/(100+25)+(100-20) [100*5-2*25*20]/125+80 (500-1000)/205= 100/41 Ans
• Ex.7 A man sold 2 articles at the same price on first he gains 20% and in other he lost 20% then find the overall profit/Loss.

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  Sol. SP1 = SP2 120 CP1 = 80 CP2 CP1/CP2= 80/120 = 2/3 CP is 2+3 = 5 Profit or loss = 2 *(20/100) - 3 *(20/100) = -1/5 loss Loss = (-1/5) * (100/5) = 4% Alternate formula when sale price is same = (r)^2/100 = (20)^2/100 = 400/100 = 4% Ans
• Ex.8 A man sells a book at a profit of 20% if he had purchased it 20% less and sold it 18 Rs. less then he has gained 25% find the cost price of the article.

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  Sol. method 1. CP1 = 100% SP1 = 120% CP2 = 80% SP2 = 80 * (125/100) = 100% 20% difference is in between SP1 and SP2 20% = 18 Rs. 100% = 18*(100/20) = 90 Ans Method 2 20% = 1/5 -> equivalent fraction 25% = 1/4 The difference between SP1 and SP2 is 1 1 = 18 5 = 90 RS. Ans
• Ex.9 The profit earn by sold an article for 1920 Rs. is equal to the loss after selling the same article at 1280 Rs. then what price it should be sold to gain a 25% profit.

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  Sol. Profit = loss SP - CP = CP - SP 1920 - CP = CP - 1280 2CP = 3200 CP = 1600 100% = 1600 125% = 1600 *(125/100) 2000 Ans
• Ex.10 If SP of 20 articles is equal to the CP of 25 articles find profit and loss percent.

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  Sol. 20 SP = 25 CP SP/CP = 5/4 Profit = (1/4) * 100= 25% Ans
• Ex.11 After selling 72 article man earn a profit of SP of 9 articles then find the profit.

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  Sol. P = SP - CP 9 SP = 72 SP - 72 CP 8 CP = 7 SP SP/CP = 8/7 1/7 = 14 ⅔ Ans