PROFIT AND LOSS. IMPORTANT CONCEPTS 1. Cost price and selling price Cost price (CP) is the price at which an article is purchased.

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Jayson Franklin
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2 PROFIT AND LOSS IMPORTANT CONCEPTS 1. Cost price and selling price Cost price (CP) is the price at which an article is purchased. Selling price (SP) is the price at which an article is sold. 2. Profit and loss If selling price is more than cost price, profit (gain) occurs. If selling price is less than cost price, loss occurs. In case of profit, Profit = selling price cost price selling price = cost price + profit cost price = selling price profit In case of loss, Loss = cost price - selling price selling price = cost price - loss cost price = selling price + loss 3. Profit percentage and loss percentage Profit percentage and loss percentage are always calculated on cost price unless otherwise stated. In case of profit, Profit percentage=profit 100/cost price Selling price = cost price+ (cost price profit percentage)/100 = cost price (100+profit percentage)/100

3 Cost price=100 selling price/ (100+profit percentage) Example: If an object is sold at a profit of 20%, selling price =120% of cost price In case of loss, Loss percentage = loss 100/CP Selling price = CP ((CP x Loss Percentage)/100) = CP (100 Loss Percentage)/100 CP = (100 * Selling Price)/ (100 - Loss Percentage) Example: If an object is sold at a loss of 20% Selling price =80% of cost price 4. Selling at same price (4.1)Suppose a person sells two objects at the same price, one at a profit of x1% and another at a profit of x2% Then, Net profit percentage =100(x1+x2) + 2x1x2 / (200+x1+x2) Note: (a) For loss, use -sign for x1 and/or x2 as applicable. (b) If the formula evaluates to a negative value, it means there is a net loss Example 1: Two objects are sold at the same price, one at a profit of 10% and another at a profit of 32%. Then, (100(10+32) )/ ( )=20% i.e., there is a net profit percentage of 20% Example 2: Two objects are sold at the same price, one at a profit of 40% and another at a loss of 16%.Then,

4 (100(40 16) ( 16))/ ( ) = 5% i.e., there is a net profit percentage of 5% Example 3: Two objects are sold at the same price, one at a profit of 20% and another at a loss of 28%. Then, (100(20 28) ( 28))/( ) = 10% i.e., there is a net loss percentage of 10% (4.2) suppose a trader sells two objects at the same price, one at a profit of x% and another at a loss of x%. Then he always incurs a net loss expressed as net loss percentage =(x/10) ^2 Example: Two objects are sold at the same price, one at a loss of 22% and another at a loss of 22%. Then, Net loss percentage = (22/10) ^2 = 4.84% Marked price and discount The price on the label of an article is called its marked price (list price). The deduction on the marked price is called discount. Selling price = marked price - discount discount = marked price - selling price marked price = selling price + discount Note: (a) If there is no discount, the marked price is equal to the selling price (b) Discount is always calculated on marked price unless otherwise stated.

5 Discount percentage: Discount percentage is the discount expressed as a percent of marked price. Discount percentage = discount 100/marked price Selling price = marked price (marked price discount percentage)/100 = marked price (100 discount percentage)/100 Marked price = (100 selling price/100 discount percentage) Successive discounts If d1%, d2%, d3% are successive discounts on marked price, Selling price = marked price (100 d1/100)(100 d2/100)(100 d3/100) SPECIAL CASES 1. If cost price of x articles is same as selling price of y articles, profit percentage = (x y)100/y Proof: Let cost price of x articles == selling price of y articles = k cost price of 1 article = k/x selling price of 1 article = k/y profit percentage = ((k/y k/x)*100)/(k/x) = (x - y)*100/y Example 1: If cost price of 15 apples is equal to selling price of 10 apples, what is the profit/loss percentage?

6 (15 10)100/10 = 50% i.e., there is a profit of 50% 2. A trader purchases m1 articles for n1 and sells m2 articles for n2 Then, Profit percentage = ((m1*n2/m2*n1) 1)*100 Example 1: 9 books are purchased for Rs. 10 and 15 books are sold for Rs. 17. Find profit/loss percent. ((9 17/15 10) 1)100 = 2% i.e., net profit percent = 2% 3. A person buys two articles for x. He sells one at a profit of p% and the other at a loss of l%. If each item was sold at the same price, then Cost price of the article which was sold in profit = x(100 l)/(200 + p l) Cost price of the article which was sold in loss = x(100 + p)/(200 + p l) Example: John purchases two cycles for Rs He sells one at a loss of 20% and other at a gain of 25%. If both the cycles are sold at the same price, find the cost price of each cycle. Cost price of the cycle which was sold at loss = 4100( )/( ) = Rs cost price of the cycle which was sold at profit = 4100(100-20)/( ) = Rs Using false weights

7 If a trader uses faulty measure of f units instead of t units and sells his goods at a profit of x%, net profit percentage = (100(t f) + tx)/f Note: (a) For loss, use -sign for x (b) If the formula evaluates to a -ve value, it means there is a net loss Example 1: A trader sells his goods at 20% profit. He uses a weight of 450 gm instead of 500 gm. Find his overall profit/loss percentage. (100*( ) )/450 = 33.33% i.e., required profit percentage = 33.33% If a trader uses faulty measure of f units instead of t units, but professes to sell his goods at cost price, net profit percentage = 100(t f)/f Example 1: A trader professes to sell his goods at cost price. But he uses a weight of 95 gm instead of 100 gm. Find his overall profit/loss percentage. 100*(100 95)/95 = 100/19% i.e., required profit percentage = 100/19%

Quantitative Aptitude 10. PROFIT AND LOSS

Quantitative Aptitude 10. PROFIT AND LOSS 10. PROFIT AND LOSS Cost Price: The price at which an article is purchased, is called the cost price or CP. Selling Price: The price at which an article is sold is called the selling price or SP. Formulae: