Profit% and Loss% are always calculated on Cost price. ) Cost Price. Above formula is useful for solving several problems in Profit and Discounts.

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1 Profit = Selling price (S. P) Cost price (C. P) Loss = Cost price (C. P) Selling price (S. P) Profit percentage (P %) = Loss percentage (L %) = Profit Cost Price Loss Cost Price Selling price (S. P) = +Profit % Cost price Selling price (S. P) = Loss % Cost price NOTE: Profit% and Loss% are always calculated on Cost price Discount = Marked Price Selling Price Discount % = Discount Marked Price Marked Price = ( +Profit % ) Cost Price Discount % Above formula is useful for solving several problems in Profit and Discounts. Discount is always calculated on Marked Price / Labelled Price. Shopkeeper will label his price with certain % above CP. SP = Marked Price Discount. Profit / Loss is always calculated on Cost Price. SP = CP + Profit Now SP = MP [ SP = CP [ D% + P% ] ] These two are the basic formulae and the other formulae can be derived from these. Usual sign convention is + for profit and for loss and always fordiscount. If X 1 and X 2 both are the rates of gain or both are the rates of loss, then C. P = ( ) Amount of difference between S. P X1 X2 If in X 1 and X 2 one is the rate of gain and another one is rate of loss, then C. P = ( ) Amount of difference between S. P X1 + X2 1 Mohan sold an item for 4510/- and incurred a loss of 45%. At what price should he have sold the item to have gained profit of 45%.? Short method for selling price S. P ( Profit % Loss % ) 4510 ( ) = 11890

2 Here, loss% => 45 = 55% Profit% = + 45 = 145% = 11890/- (answer) 2 Ramya purchased an item for 46000/- and sold it at loss of 12% with that amount she purchased another item and sold it a gain of 12%. What was her overall gain or loss? Short method for cost price C. P LOSS% PROFIT% = => Here, loss% => 12 = 88% Profit% => + 12 = 112% = Therefore, = loss (answer) 3 In a sale perfumes are available at a discount of 25% on the selling price. If a perfumes cost 5895/- in the sale, what is the selling price of the perfume? Let selling price of perfume = X X 75 = 5895 (discount = 25%) X = 7860 (answer) 4 A man purchased 25 apples for 20/- and sold 20 apples for 25/-. Find profit %? SHORT METHOD: = % (answer) Profit % = On selling 17 balls at 720/- there is a loss equal to the cost price of 5 balls. Then find the cost price. C.P S.P = LOSS C.P of 17 balls S.P of 17 balls = C.P of 5 balls C.P of 12 balls = S.P of 17 balls = 720 Therefore, C.P of 12 balls = 720 One ball = = 60 (answer)

3 6 A man purchased some eggs at for 5/- and sold them at 5 for 12/-. Thus he gained 143 in all. The no. of eggs he bought is C.P of one egg = 5 3 rupee S.P of one egg = 12 rupee Gain in one egg => 12 Let no. of eggs = X ( 12 5 ) X = X = 195/- (answer) By selling an article a man makes a profit of 25% of its selling price. His profit % is. Let S.P = X, then profit % = X 25 = X/4 C.P = S.P PROFIT C.P = x x 4 = 3x 4 Therefore, profit % = Profit = X 4 3X 4 = 33 1/3 % (answer) C.P 8 An article is listed at 920/-. A customer pays /- for it after getting two successive discounts. If the rate of first discount is 15%, the rate of second discount is. Marked price = 920/- After getting two successive discounts it becomes / ( x ) = X = 5% (answer) 9 By selling an article at 80% of the marked price, there is a loss of 10%. If the article is sold at the marked price, the profit % will be Let C.P = X & Marked price = Y Then S.P = Y 80 For loss %, y 80 = 90 x

4 Required Profit % = ( y x x ) X = 12.5% (answer) y = 9x 8 9x = ( 8 x ) x 10 The marked price of a Radio set is 480/-. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed his gain % would be.. After discount, S.P = = 432/- As profit is 8%, then C.P => 432 = 108 C. P C.P = 400/- So without discount, Profit => = 80/- Profit % = = 20% (answer) 11 How much percent more than C.P should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price he gains 20%.? Formula = X + Y + XY X 25 X 25 = 20 X = 60% (answer) 12 A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed. The ratio of the C.P to printed price of the book. Formula Marked Price = ( + Profit %) Discount % ) Cost Price Here, profit % (P %) = 112% ( + 12) Discount % (D %) = 90% ( - 10) M. P = C. P Required ratio C.P M.P = (answer) 13 A trade man sold an article at a loss of 20%. If the S.P had been increased by /-, there would have been a gain of 5%. The C.P of the article is

5 Let C.P = X, then S.P = X 80 And new S.P = X 105 X = 400/- (answer) 105 X 80 Y = 14 20% loss on selling price is what percent loss on the cost price? Let S.P =, then C.P = 120 Then, loss => 120 = 20/- Therefore, loss % = = 16 2/3 % (answer) 15 By selling an article for 144/- a person gained such that the percentage gain equals the cost price of the article. The cost price of the article.. Let C.P = X & profit % = C.P Formula S. P = C. P ( + X 144 = X ( ) X = 80/- (answer) + Profit % ) 16 If the selling price of the article is doubled, then its loss % is converted into equal profit %. The loss % of the article is Let loss = X, & C.P = /-, then S.P = -X New S.P = 2(-X) and profit % = X % 2 ( X) = + X X = % (answer) 17 A trader sells an article at a profit of 30%. Had he purchased it at 10% less and sells for 330/- less he would have gained 20%. Find the C.P. Let C.P = X, then S.P = X 130 New C.P = X & New S.P = X - 330

6 X = X 120 X = 1500/- (answer) 18 By selling toffees at rate of 20 for 10/-, a man loses 4%. To gain 20%, how many toffees must be sold for 10/-? Short method If x. = 96% (loss% => 4 = 96%). = 120% (Profit% => + 20 = 120%) X = 16 toffees (answer) 10 X = If on a marked price the difference of selling price with a discount of 30% and two successive discounts of 20% and 10% is 72, then the Marked Price is. Successive discount = 28% Let marked price = X X 30 X 28 = 72 X = 3600/- (answer) 20 A reduction of 20% in the price of an apple enable a man to buy 10 apples more for 250/-. Te reduced price of apples per dozen. Formula Reduced price of an apple = X Y Z Here, X = 20% (reduction), Y = 250/- and Z = 10 (more apples) = 10 = 5/- Therefore, reduced price of an apple for dozen = 12 5 = 60/- (answer) 21 While selling a watch, a shopkeeper gives a discount of 5%. If he gives a discount of 6%, he earns 15/- less as profit. What is the marked price of watch?

7 Let marked price = X X = 1500/- (answer) 95 X 94 X = Krishna purchased a no. of articles at 10/- for each and the same number for 14/- each. He mixed them together and sold them for 13/- each. Then his gain or loss% is? Total C. P of articles = = 12/- 2 S. P = 13/- Then profit => S. P C. P = = 1/- Profit% = 1 12 = % (answer) 23 A man sells an article at 5% above its C. P. If he had bought it at 5% less than what he paid for it and sold it for 2/- less, he would have gained 10%. Find the C. P of the article Let C. P = X, then new C. P = x 95 And S. P when it sells 2/- less = 105 X 2 According to formula, S. P = C. P (+ Profit %) / X 2 = = 400/- (answer) X 110 X 24 Pure ghee costs /- per kg. After adulterating it with vegetable oil costing 50/- per kg a shopkeeper sells the mixture at the rate of 96/- per kg thereby making a profit of 20%. In what ratio does he mix the two?v Mean price (C. P) = = 80/- per kg By the rule of Allegation & Mixtures

8 Required ratio => 30 : 20 = 3 : 2 (answer) 25 A fruit seller has 24 kg of apples. He sells a part of these at 20% gain and the balance at a loss of 5%. If on the whole he earns a profit of 10%, the amount of apples sold at loss is By the rule of Allegation & Mixtures Required ratio => 15: 10 = 3: 2 Therefore, the amount of apples sold at loss is => = 9.6/- (answer) 26 If the selling price of 24/- results in a 20% discount o the list price, what selling price would result in a 30% discount on list price? SHORT METHOD If 80% ( 20).. = 24 70% ( 30). =? = 80 = 21/- (answer) 27 What percentage on profit on cost price equals 30% of profit on selling price? If C. P = /- And Gain = X Then S. P = ( + X)/- Here, formula is Gain Gain% = Selling Price

9 X 30 = +X X = 42 6/7 % (answer) 28 A dealer marks his goods 30% above his C. P and then allows 15% discount on it. What is the C. P of an article on which he gains 84/-? Let C. P of articles = X/- M. P => X 130 = 13x 10 Selling Price = Marked Price ( Discount% ) S. P = 13X S. P = 221x 200 Gain = S. P C. P 84 = 221X X 200 X = 800/- (answer) 29 A man purchased 150 pens at the rate of 12/- per pen. He sold 50 pens at a gain of 10%. The percentage gain at which he must sell the remaining pens so as to gain 15% on the whole outlay is Required S. P of 150 pens = = 2070/- S. P of first 50 pens = = = 660/- Required S. P of pens => = 1410/- C. P of pens => 12 = 1200/- Gain = S. P C. P = Gain = 210/- Gain Gain% = Cost Price Gain% = = 17 ½ % (answer) 30 A sells an article to B making a profit of 1/5 of his outlay. B sells it to C gaining 20%. If C sells it for 600/- and incurs a loss of 1/6 of his outlay, then C. P of A is Let C. P of article = X

10 SHORT METHOD: 600 = x Here, profit = = 6 5, loss = = 5 6 X = 500/- (answer) 31 Nitin bought some oranges at 40/- a dozen and an equal numbers at 30/- a dozen. He sold them at 45/- a dozen and made a profit of 480/-. The no. of oranges, he bought was Let the no. of oranges bought be 2X (X + X) dozens Total C. P => 40X + 30X = 70X Now total S. P => 45 2 = 90X Profit = S. P C. P 480 = 90X 70X X = 24/- Therefore, no. of oranges bought = 2 24 = 48 dozens (answer) 32 A shopkeeper marks his goods at 40% above their C. P. He is able to sell 3/4th of his goods at this price, and the remaining at 40% discount. Assuming that the shopkeeper is able to sell the goods he buys, find his loss or gain as % on the whole transaction Let total C. P = /- ( articles) Then, total S. P = = 126/- Gain 26 (126- ) Therefore, Gain% = 26 (answer) 33 An article is sold at a gain of 15%. Had it been sold for 27/- more, the profit would have been 20%. The C. P of the article is SHORT METHOD: PERCENTAGE METHOD: Difference => = 5% 5% (if). 27 %? 27 = 5 = 540/- (answer)

11 34 Half of articles were sold at a profit of 20% and the rest of a profit of 40%. If all the articles had been sold at a profit of 25%, the total profit would have been less than earlier profit. The C. P of each article was Let C. P of an article = X (Total C. P = X) S. P of 50 articles = 5X 120 = 60X S. P of remain 50 articles = 50X 140 = 70X S. P of articles => 60X + 70X = 130X And, new S. P => X 125 = 125X 130X 125X = X = 20/- (answer) 35 A certain no. of articles were purchased for 90/-. Three more articles could have been purchased for the same amount if each article was cheaper by 1/-. Find the no. of articles purchased Let the no. of articles = X X = 15/- (answer) 90 X 90 X + 3 = 1 36 A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% o the discounted price. If a customer pays /- as the price of the item including sales tax, find the marked price of the item Let the M. P = X, discount = 10% Discounted price => X 90 = 9X/10 Sales tax = 8% Therefore, S. P = 9X 10 X = 700/- (answer) 108 9X =

12 37 A bicycle agent allows 20% discount on his M. P and then makes a profit of 20% on his outlay (C. P). What is the M. P of the bicycle on which he gains 40/-? Let M. P = X, C. P = Y Discount = 20% (given), profit = 20% (given) and Gain = 40/- (given) S. P = X 80 = 4x 5 And Y = 2x 5 Gain = S. P C. P 40 = 4X 5 2X 5 X = 300/- (answer) Discount% [ S. P = M. P ] 4X 5 = Y Profit% [S. P = C. P ] 38 The marked price of an article is 50% above cost price. When marked price is increased by 20%, the profit doubles. If original marked price is 300/-, then original selling price is Let original S. P = X C. P of article => 300 = 200/- (from question) 150 X = 2(X 200) X = 250/- (answer) 39 If books bought at prices ranging from /- to 350/- are sold at prices ranging from 300/- to 425/-. What is the greatest possible profit that might be made in selling 8 books? Least C. P => = 1600/- Greatest S. P => = 3400/- Required profit => = 1800/- (answer) 40 The price of a sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in consumption and the original consumption is The raised price = 120 of the former pric So, the house holder must now consume / 120 of the original amount So, the reduction in consumption

13 = (1 ) of the original consumption 200 = 1/6 of the original consumption (answer) 41 A man bought some oranges at 10/- per dozen and bought the same no. of oranges at 8 per dozen. He sold these oranges 11/- per dozen and gained 120/-. The total no. of oranges bought by him was C. P of 2- dozen oranges => (10 + 8) = 18/- S. P of 2- dozen oranges => ( ) = 22/- If profit is 4/- (22-18), then oranges bought = 2 dozen If profit is 120/-, then oranges bought =? = 4 = 60 dozens (answer) 42 A girl buys 2- pigeons for 182/-. She sells one at a loss of 5% and another at a profit of 8%. But she neither gains nor loss on the whole. Find the price of pigeon which has sold at a profit The ratio of price of pigeons sold at loss and profit respectively are in the ratio = 8 : 5 5 Cost price of profitable pigeon is = = 70/- (answer) 43 How many kilograms of rice costing /- per kg must be mixed with 126 kg of rice costing 8. 55/- per kg so that 20% may be gained by selling the mixture at /- per kg? S. P of one kg mixture = /- Gain = 20% Then, C. P = = 12/- Dearer price: Cheaper price => 345: 630 = Let X- kg of dearer may be mixed with 126 kg of cheaper Then, X = X = 69 kg (answer)

14 44 In a big bazaar, a shopkeeper mixed two varieties of Daal at 20/- per kg an 30/- per kg in the ratio 2: 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture C. P of mixture = 2+3 = 26/- S. P of the mixture => = /- (answer) 45 Gauri went to stationary and bought things worth 25/- out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Let the amount taxable purchase = X/- Then 6% of X = 30 X = 5/- Cost of tax free items = [25- ( )] = /- (answer) 46 A person buys certain no. of marbles at 20 per rupee are equal no. of marbles at 30 per rupee. He mixes them and sells them at 25 per rupee. His gain or loss in the transaction is C. P of each 20 per rupee = 1 20 C. P of each 30 per rupee = 1 30 Average cost price of each marble = According to the question S. P of each per rupee = 1 25 Here, 1 > 1 => means, loss Therefore, loss % = ( ) Loss % = 4% (answer) 47 A man purchased a table and a chair for 1300/-. He sold the table at a profit of 20% and the chair at a profit of 25%. In this way, his total profit was 23 1/3 %. The cost price of the table

15 C. P of the table = X C. P of the chair = X Profit on table + profit on chair = total profit X (1300 X) = 231 3% of 1300 X = /- (answer) 48 Titan sells a wrist watch to a wholesaler making a profit of 10%. The wholesaler in turn, sells it to the retailer making a profit of 10% a customer purchases it by paying 990/-. Thus, the profit f retailer is 25/11 %. What is the cost incurred by the titan to produce it? Let C. P of Titan = X X X = 800/- (answer) = A shopkeeper sold 12 cameras at a profit of 20% and 8 cameras at a profit of 10%. If he had sold all the 20 cameras at a profit of 15%, then his profit would have been reduced by 36/-. What is the cost price of each camera? Let C. P of each camera = X S. P of 12 cameras sold at 20% = X = 144X 10 S. P of 8 cameras sold at 10% = X = 88X 10 X = 180/- (answer) 36 = 144x x 10 23x 50 A cycle is sold at a profit 15%. If both cost price and selling price are decreased by 200/- the profit would be 5% more. What is the original cost price of cycle? Let the original C. P = X So, S. P = X 115 = 23x 20

16 Now, new C. P = X 200 Then, new S. P = 23X Profit = S. P C. P = 23X (X 200) Profit = 3X 20 Profit Profit % = Cost price 20 = ( 3X 20 3X ) X = 800/- (answer) 51 A sells an article to B making a profit of 1/5th his outlay. B sells it to C, gaining 20%. If C sells it for 600/- and incurs a loss of 1/6th his outlay, the C. P of A is Let the C. P of A = X X ( ) 120 (1 1 6 ) = 600 X = 500/- (answer) 52 A man sold an article for 75/- and lost something. Had he sold it for 96/- his gain would have been double the former loss. The cost price of the article is Let C. P = X 96 X = 2 ( X 75 ) X = 82/- (answer) 53 A reduction of 25% in the price of eggs will enable one to buy 4 dozens more eggs for 96/-. What is the price per dozen? Let original price = X New price per dozen = X 75 X = 8/- (answer) => 3X X 4 96 X = 4 54 An article sold at a gain of 15%. Had it been sold for 27 more, the profit would have been 20%. The C. P of the article is

17 PERCENTAGE METHOD: If 5% (20% - 15%) = 27 % =? = ( 27 5 ) = 540/- (answer) 55 A retailer bought 90 pens for 40/- each. He sells 30 of them at a gain of 12%. What must be the gain% of the remaining pens so as to get 15% gain on the whole? Let the required gain% be X%. Then, (90 30) X = X = 16.5% (answer) 56 The cost price of 5 articles is equal to the selling price of 4 articles. What is the profit or loss %? If we assume CP of 5 articles = SP of 4 articles = Rs. CP of one article = Rs. 20 SP of one article = Rs. 25 Profit = Rs. 5 Profit % = 5 20 = 25% (answer) 57 A shopkeeper sold two Televisions of different make for Rs each. On one, he got profit of 20% and on other, he attained loss of 10%. What is the net profit percentage? Here P = 20% = x%, L = 10% = y% 2 (+x)(+y) Overall Profit / Loss % = [ ]% (+x)+ (+y) (Use + when there is profit and when there is loss) = [ ]% 210 = 2 6 % (profit since the result is positive) 7

18 58 A shopkeeper sold some articles at Rs.35 per article and gained 40% on it. What would be the selling price of each article to get 60% profit? Use SP 1 = SP 2 analogy for such type of problems +x +y = SP => SP 2 = Rs. 40 PERCENTAGE METHOD: OR If 35/- per article (gain 40%) Then X/- per article (gain 60%) X = 160 X = 40/- (answer) 59 A trader bought two horses for 19, 500/-. He sold one at a loss of 20% and the other at a profit of 15%. If the selling price of each horse is the same, then their cost prices are respectively. Let Cost Price of one horse = x/-, then of other 19, 500 x One horse sold at loss of 20%, other at 15% gain. Selling Price is same 80% of x = 115% of (19, 500 x) 80 x = 115 (19, 500 x) x = 11, 500/ (answer) Cost price of other = 19, , 500 = 8, 000/- (answer) 60 A shopkeeper gave an additional 20% concession on the reduced price after giving 30% standard concession on an article. If Arun bought that article for 1, 120/-, what was the original price? Let original price = x/- x = 1120

19 X = 2, 000/- (answer) 61 A reduction of 20% in the price of sugar enables a person to obtain 40 kg more for 210/-. What is the reduced price per kg? Owing to the fall in price, there is a saving of 20% on 210/- i.e 42/- So, for 42/-, a person purchases 40 kg of sugar. Hence, reduced price per kg = 42 = 1.05/- (answer) A article sold at 30% profit. Had it been sold at 155/- more than previous selling price and the cost price were also increased by /- then profit would have been 5% more. Then find the cost price of the article Let cost price of article = x Selling price of article = 130x Increased cost price = (x + ) Increased selling price = (130x + 155) Profit = Profit = Selling price Cost price Cost price (130x + 155) (x + ) (x+) By solving, we get x = 4 Therefore, Cost price of article = 4 = 400 (answer) 63 Ram sells onions in the streets of Varanasi. Due to recent shortfall in the supply of onions, he doubles his selling price despite the cost price remains same for him due to a fixed contract. He realizes that his profit has tripled. Find the profit percent. Let original Selling price be SP and Cost price be CP Then, 2SP CP = 3(SP CP) SP = 2CP Hence, original profit % = % (answer) 64 A loss of 19% gets converted into a profit on 17% when the selling price is increased by 162/-. The cost price of the article is.. SHORT METHOD Loss (-19%) Profit ( +17%) Difference => 17 (- 19) = 36%

20 If 36%. 162 Then %.? = 450/- (answer) 162 = On selling a Pen at 5% loss and a book at 15% gain, Rajini gains 7/-. If he sells the pen at 5% gain and the book at 10% gain, then he gains 13/-. The actual price of the book is. Let the C. P of a pen = x/- and that of a book = y/- 15y 5x = 700. (1) And, 10y + 5x = 130. (2) From equations (1) and (2), we get y = 80/- Therefore, C. P of a book = 80/- (answer) 66 A article is sold at profit of 25%. Its CP and SP are more by 20 and 4 respectively. The percentage of profit decreased by 15%. Find the Cost price Let Cost price = x Selling price = 5x 4 ( 5x 4 + 4) (x + 20) = (x + 20) 10 x = 120/- (answer)

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: