Quantitative Methods Chapter 4 – PROFIT & LOSS Pranjoy Arup Das

Session 5,

Profit is earned when something is bought at Rs. X and sold at an amount higher than Rs. X, say Rs. (X+Y) Here Rs. X is called the Cost Price (CP), Rs. (X+Y) is called the Selling Price (SP) and the difference between the SP and the CP is the profit, i.e. (X+Y) – X = Rs. Y. Eg. If a car is bought for Rs. 3,50,000 and sold for Rs. 4,00,000, a profit of Rs. (4,00,000 – 3,50,000) = Rs. 50,000 will be earned. Profit is the excess of SP over the CP, i.e., SP – CP. Also called Gain. Profit % = (Profit / CP) * 100 = {(SP – CP) / CP} * 100 Loss is incurred when something is bought at Rs. X and sold at an amount lower than Rs. X, say Rs. (X – Y). Here the SP is lower than the CP and as such a loss of Rs. Y is incurred, i.e., Loss = Rs. X – (X – Y) = Rs. Y. Eg. If a car is bought at Rs. 3,50,000 and sold at Rs. 3,20,000 a loss of Rs. ( ) = Rs will be incurred. Loss is the deficiency of SP from the CP, i.e., CP – SP Loss % = (Loss / CP) * 100 = {(CP – SP)/CP} * 100

Ex 1. Page 219 A desk is bought for Rs. 475 and sold for Rs Find the gain %. Solution: Here Cost Price = Rs. 475 & Selling price = Rs. 570 As SP > CP, a profit is earned. Profit or Gain = 570 – 475 = Rs 95 Gain % or Profit % = Profit / CP * 100 = (95/475) * 100 = Rs_______ Ex. 3 A Bed sheet is sold for Rs. 405 at a gain of 8%. Find its CP. Solution: If a gain of 8% is earned, that means if CP = Rs. 100, SP will be Rs. 108 So it can be said that when the SP is Rs. 108, the CP is Rs. 100 When SP is Rs. 405, CP = (100/108) * 405= Rs. ________

Ex. 7 Solution: By selling 100 pens, a stationer earns a profit equal to the selling price of 20 pens. Find his gain percent. Let the SP per pen be Rs. x SP of 100 pens = Rs. 100x. And SP of 20 pens = Rs. 20x, which, as mentioned, is the profit. Now we know that, SP- CP = Profit That means: SP of 100 pens – CP of 100 pens = Profit, which is the SP of 20 pens => 100 x – CP of 100 pens = 20x => CP of 100 pens = 100x – 20 x = Rs. 80x Now, if Profit is Rs. 20x and CP is Rs. 80x Profit % = (20x / 80x) * 100 = _____%

Ex. 8 Solution: Bananas are bought at 6 for Rs. 5 and sold at 8 for Rs. 11. Find the gain or loss percent. Let the total no. of bananas be x. CP of 6 bananas is Rs. 5 So CP of x Bananas will be = (5/6) * x = Rs. 5x/6 Again, SP of 8 bananas is Rs. 11, So SP of x bananas will be = (11/8) * x = Rs. 11x/8 Profit ? Or Loss ? Clearly there is a profit. ( 5/6 = 0.83 which is less than 11/8 = 1.38) Profit = (11x/8) – (5x/6) = 13x/24 So Profit % = =

Ex. 9 Solution: Selling price of 10 apples is the same as the Cost price of 8 apples. Find the gain / loss percent. Let the CP of 8 apples & SP of 10 apples be Rs. x CP per apple = Rs. x/8 And SP per apple = Rs. x/10………………………….Gain? Loss? Clearly there is a loss ( As 1/10 is less than 1/8) So, Loss = x/8 – x/10 = Rs. x/40 Loss % = =

Ex. 11 Solution:A man sold two cows for Rs /- each. On one he gains 15% and on the other he loses 15%. Find his overall gain or loss percentage Total SP of Cow A & Cow B = Rs. ( ) = Rs If sale of Cow A brings profit of 15%, that means if the cost is Rs. 100, the SP is Rs. 115 So if SP is Rs , the CP will be (100/115)* 15640= And If the sale if Cow B results in loss of 15%, that means if the cost is Rs. 100, the SP is Rs. 85 So if the SP is Rs , the CP will be (100/85)*15640= So the total CP of the two cows = There is a loss incurred from the sale of the two cows. Overall loss = Overall Loss % = /32000 * 100 Rs Rs Rs = Rs Rs. (32000 – 31280) = Rs.

Concept of Marked Price: Usually sellers deliberately increase their CP higher than their required profit level and then offer discounts on this increased price This increased price is called the marked price or the list price (MP). The marked price after discount becomes the selling price (SP). Marking prices and then allowing discounts helps sellers to attract customers and also earn the required profits inspite of the discounts. Marked Price – Discount = Selling Price Discount = MP – SP Discount % = (Discount / Marked Price) * 100 Important points to remember: Discount is always based on the Marked Price. Profit is always based on the Cost Price. CP + Profit = SP Profit % = Profit /CP *100

Ex. 12 A trader lists his items at 15% above cost price and allows a discount of 8% on cash payment. Find his gain or loss percent. Solution: Let the CP be Rs. x The list price or marked price(MP) = 115% of x = Rs.(115x/100) So, Discount = 8% of (115x/100) We know that SP = MP – Discount => SP = (115x/100) – 8% of (115x/100) => SP = So the gain or profit = SP – CP = And the profit % = Profit / CP * 100 = Rs. (529x/500) Rs. (529x/500) – Rs. x Rs. (29x/500)

Ex. 14 Solution: Sunil buys an article with 25% discount on its marked price. By selling it for Rs. 330, he makes a profit of 10%. Find the marked price. Let the MP be Rs. x That means Sunil bought the article for 75% of Rs. X = Rs. 75x/100 Now Sunil adds 10% to the price at which he bought the article and that becomes his selling price. i.e Rs Sunils SP of the article = 110% of (75x/100) => 330 = => x = Rs. ________________

Ex. 15 Solution: A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If the marked price is Rs. 1200, find the cost price. Let the CP be Rs. x Since the dealer makes a profit of 20%, the SP = 120% of x = Rs. 120x/100 The MP = Rs Since the dealer offers a discount of 10%, The SP = 90% of 1200 = Rs So from the above it is clear that 120x/100 = 1080 => x =_______________

Pr no. 76 Page no. 229 (RSA) A shopkeeper marks his goods at 20% above the cost price and allows some discount on it in such a way that he gains 8%. What is the rate of discount? Solution: Let the CP be Rs. x Since the shopkeeper marks his goods at 20%, His MP = 120% of x = Rs. 120x/100 Since the shopkeeper makes a profit of 8%, the SP = 108% of x = Rs. 108x/100 So his discount amount = 120x/100 – 108x/100 = ________ Rate of discount or discount % = ___________

RECAP: Profit amount= SP – CPLoss amount= CP – SP Profit % = {(SP-CP) / CP} * 100Loss % ={(CP – SP) / CP}*100 x% profit means CP + (x% of CP) = SP y% loss means CP – (y% of CP ) = SP Marked price = CP + Increased amount Marked price – Discount amount= SP Discount amount = MP – SP Discount % = (Discount amount / MP) * 100 or {(MP – SP) / MP} * 100 Review & practice session –RSA, Exercise 11A, Page 223 problem nos. 1, 2, 5, 6, 8, 9, 16, 21, 24, 38, 40, 46, 49, 77, 80, 81, 83, 90, 95, 99, 104, 105.