Use the following solved examples to understand the fundamentals of profit and loss: Show Example 1: A cloth merchant bought 35 shirts, each at a price of Rs 280. He sold each of them for Rs. 308. Find his percentage profit.
 Sol: The profit percentage remains same for one unit as well for all the units. Thus the calculations should be done for one unit only. CP = Rs. 280. SP = Rs. 308. Profit = 308 – 280 = Rs. 28. Now you need to apply profit percentage formula for the same. Profit percentage = 100 × 28/280 = 10% Example 2: An article is sold for Rs 2400 at a profit of 25 %. What would have been the actual profit or loss if it had been sold at Rs 1800? Sol: Firstly let us find the cost price of the same. C.P. = 2400 × 100/125 = 1920. New selling price = Rs. 1800 ⇒ Loss = 1920 – 1800 = 120 ∴ Loss percentage = 100 × 120/1920 = 6.25%. Example 3: A retail fruit vendor buys pineapples at a score for Rs 200, and retails them at a dozen for Rs 156. Did he gain or lose in the transaction and what % was his gain or loss? Sol: C.P = Rs. 220/score ∴ C.P/Pineapple = 200/20 = 10 (Note: 1 score = 20 nos.) S.P = Rs.156/dozen ∴ S.P/Pineapple = 156/12 = 13. Profit = Rs. 3. ∴ % Profit = 100 × 3/10 = 30% Example 4: If an article is sold at a loss of 66 2/3%, what is the loss in terms of the selling price? Sol: Let the C. P. = 100. ∴ Amount of loss = 66 2/3 or 200/3 ⇒ S. P = 100 – 66 2/3 = 33 1/3 or 100/3. Example 5: Profit obtained by selling a floppy disc at Rs. 320 is equal to 7/5th of the profit obtained by selling the same floppy disc at Rs. 300. What is the cost price of the watch? Sol: Let the cost of a watch be x ∴ (320 - x) = 7/5 × (300 - x). Example 6: A man sells two chairs for Rs. 480 each. On one he makes a profit of 20 % and on the other he makes a loss of 20 %. Find his total loss/gain in these two transactions (in Rs.). Sol: Here the amount of loss can be directly found by the formula given in the formula section of this article. Example 7: Mukesh purchased two watches at the same price and sold one at a profit of 20 % and the other at a profit of 22.5%. If the difference between the two selling price is Rs 150, what is the cost price of each of the watches? Sol: Let the cost price of the watches = 100. The selling price of the first watch = 120 and the selling price of the second watch = 122.5. The difference in the selling price = 2.5 if the cost price = 100 If the difference in selling price = 150, then the cost price = 150 × 100/2.5 = Rs. 6000. Example 8: A merchant buys 30 kg of rice at Rs 40/kg, and another 20 kg of rice at Rs 30/kg. He mixes them and sells half of the mixture at Rs. 36/kg. At what price should he sell the remaining mixture to get an overall profit of 30%? Sol: Total cost for the entire quantity of rice = (30 × 40) + (20 × 30) = Rs. 1800. If his profit is 30%, then the sales realization = 1.3 1800 = Rs. 2340. He sells 25 kg at Rs. 36/kg = Rs. 900. Therefore to make the said amount of profit, he should sell the remaining 25 kg of rice at Rs. 2340 – Rs. 900 = Rs.1440 ∴ The selling price of a kg of rice for the remaining 25 kg = 1440/25 = Rs. 57.6. Example 9: What should each of the forty shirts be sold at, the cost of each of which is Rs. 500, so as to get a profit equal to the selling price of 20 of them? Sol: S.P. of 20 Shirts = S.P of 40 Shirts – C.P. of 40 Shirts Example 10: Three - eighth of 320 chairs was sold at a profit of Rs. 50 each and the rest for Rs. 33600. If the seller makes a profit of 20 % on the whole transaction, what is the cost price of each of the chair? Sol: 120 chairs were sold at a profit of Rs. 50 each. Profit on these 120 chairs = 6000. S. P. of all 320 chairs = C. P. of 120 chairs + Profit on 120 chairs + S. P. of 200 chairs = (120 × C.P) + 6000 + 33600 = (120 × C. P.) + 39600 But these 320 chairs were sold at a profit of 20 %. S. P. = 1.2 × C.P ⇒ 320 × 1.2 × C.P = 120 × C. P. + 39600 ⇒ 384 C.P = 120 C.P + 39600 ⇒ C. P. = 150. Example 11: A package tour operator allows a 25 % discount on his advertised price and then makes a profit of 20 %. What is the advertised price on which he gains Rs. 60? Sol: Profit = Selling price – Cost Price = 60. Selling price = 1.2 (C. P.) ⇒ 1.2 C.P – C. P. = 60. ⇒ 0.2 C. P. = 60 ⇒ C. P. = 300 and Selling price = 360. List price or advertised price ⇒ (0.75) = Selling price ⇒ List price = Selling price/0.75 = 360/0.75 = Rs. 480. Example 12: A manufacturer estimates that on inspection 20% of the articles he produces are rejected. He accepts an order to supply 20,000 articles at Rs. 7.50 per item. He estimates the profit on his outlay to be 20 % after providing for the rejects. Find his cost of manufacture per article. Sol: S.P = Rs. 7.5 per item × For 20,000 items = 150,000 Minimum no. of items that need to be produced so that after providing for 20 % rejection he still has 20,000 items = 20000/0.8 = 25,000. As he makes a profit of 20%, then his cost price will be = 150000/1.2 = Rs. 125000. Now he is producing 25000 units at a cost of 125000, thus the CP per item = 125000/25000 = Rs. 5. Example 13: A man sold Pentium computers at a profit of 6 %. Had he made a loss of 5 % instead due to a price crash, he would have sold it for Rs 3,850 less. What was his cost price and selling price in each of the instances? Sol: C. P. (1.06) = S.P.1 Example 14: Trader A offers a discount of 25 % on the marked price for cash purchase. Trader B offers a trade discount of 20 % and a cash discount of 5 % on the same article marked at the same price as that of Trader A. As a buyer whom should I buy from if I am to pay cash?
Sol: Trader A: If the marked price = 100 then the net price to the buyer = 0.75 × 100 = 75. Trader B: If the marked price = 100, then the net price = 0.8 × 100 = 80 and the cash price = 0.95 × 80 = 0.76. Since the discount is higher or the price to me as a buyer is lower with Trader A, I should choose to buy from Trader A.
Using an example: Suppose we had a big animal sanctuary for cats and dogs. We had say 30 cats and 50 dogs So by proportion we have: #color(blue)("Using format type 1")# #"cats : dogs " ->30:50->3:5# as ratio (proportions) But for #3:5# we have 3 parts in combination with 5 parts giving a proportion total of #3+5=8# Converting this to fractions and hence percentage Cats #=5/(3+5)=5/8->5/8xx100% = color(white)("ddd")ul(62.5%" of the whole" # #color(white)("ddddddddddddddddd")"Added up "->100.0%" all of the whole"# Cost Price: The price at which an article is bought or purchased is called its cost price. (C.P.) Selling Price: The price at which an article is sold is called its selling price. (S.P.) Profit: When an article is sold for more than what it costs, we say that there is a ‘profit’ or gain. Loss: When an article is sold for less than what it costs , we say that there is a ‘loss’. When the selling price is equal to the cost price, then there is neither profit nor loss. We recall a few important facts below:
Caution: Profit or loss per cent is never calculated on the number of items sold, but on the cost prices of the items. In calculating any percentage change, the increase or decrease is expressed as a percentage of the first value. Buying comes before selling , thus, profit or loss is expressed as a percentage of the buying price ( i.e., the cost price ) and not of the selling price. Overheads – If there are some additional expenses incurred on the transportation , repair etc of an article purchased, they are included in the C.P. of the article and are called ‘overheads’. 3 Major Type of Profit and Loss ProblemsType 1 : Find Profit or Loss Percent.Example 1: What is the profit per cent if a table bought for is sold for ? Solution: A table is bought for and sold for . Total profit Profit % Example 2: Arun buys a T.V. for . The transportation charges are and the installation charges are . He then sells it to his friend for . Find the loss per cent. Solution: . Here transportation and installation charges fall under overhead costs. More results on S.P. and C.P.: 1. If there is a profit of then, 2. If there is a loss of then, From 1 and 2 , we derive that : 3. , when there is a profit of 4. , when there is a loss of Type 2 : Find S.P. when C.P. and Profit (or loss) Percent GivenExample 1: A man bought a T.V. set for and he sold it at a profit of . Find the selling price. Solution: Let the cost price be Then, S.P. at a profit of When C.P. is S.P. is Then, When Alternative Method: where and
Example 2: A man buys a cycle for and sells it at a loss of . Find the selling price of the cycle. Solution: Let the C.P. be Then, S.P. at a loss of When Then, when Alternative Method: where loss and
Type 3 : Find Cost Price.Example 1: Find the cost price of an article which is sold at a profit of for . Solution: , Profit % If , then If , then If , then Alternative Method: where
A few harder problems on profit and loss: Example 1: By selling a plot of land for a person loses . At what price should he sell it so as to gain ? Solution: On selling the plot for , he loses
He now wants a profit of of
Example 2: A man sells two watches at each. On one he gains and on the other he loses . What is his gain or loss per cent on the whole transaction ? Solution: S.P. of the first watch , gain C.P. of first watch Similarly, C.P. of the second watch on which he loses total C.P. of the two watches And total S.P. of the two watches net loss DiscountMarked Price: The price printed on an article or on a tag tied to it or the advertised price or the listed price is called the marked price , or, M.P. of the article. Sometimes to dispose of the old , damaged or perishable goods the retailers offer these goods at reduced prices. The retailers also reduce prices to increase the sale by reducing the marked prices of the articles. The amount deducted from the original marked prices is called ‘Retailer’s discount’ or simply ‘retail discount’ which is generally expressed as per cent or a fraction of the marked or original price. Net Price (Selling Price): The price of an article after deducting discount from the marked price is called the net price of the article. NOTE: Discount is always calculated on the marked price. In solving the problems on discount, the following formula are generally used: 1. 2. 3. If discount is , then, Example 1: The marked price of a pair of shoes is . The shopkeeper allows an off season discount of on it. Calculate – i) the discount and ii) the selling price. Solution: and i) ii) Example 2: The marked price of an article is marked above the C.P. and then it is sold at a discount of . What is the net gain per cent ? Solution: Let the of the article be more than the Exercise
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A vendor had a loss of 10% on his cost price if in a week his sale was of rs 288 what was his loss
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