Profit and Loss Aptitude Problem Question and Answer

Profit and Loss Question, Formula, Short Tricks and Notes

Suppose a shopkeeper buys an article from a manufacturer or wholesale dealer, the money paid by the shopkeeper to buy the article is called the cost price of the article. Generally we write C.P. for the cost price.  The shopkeeper sells the article which is generally more than its C.P. The price at which the shopkeeper sells the article is called the selling price of the article. Generally we write S.P. for the selling price.

C.P. Stands for Cost Price

S.P. Stands for Selling Price

 If the S.P. of an article is greater than the C.P., then the shopkeeper has earned a gain or profit.  Thus  

∴ Gain or profit = S.P. – C.P.  

Further,   C.P. = S.P. – Profit  

S.P. = C.P. + Profit  

If the S.P. of an article is less than the C.P. then the shopkeeper has suffered a loss.

 ∴ Loss = C.P. – S.P.  

Further,   S.P. = C.P. – Loss  

C.P. = S.P. + Loss

Profit or loss is always expressed as a percentage of the cost price.

Profit percent = ( profit  / C.P. )  × 100 % 

Loss percent = ( Loss / C.P. )  × 100 % 

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Example :  An article was bought at Rs. 450 and sold for Rs. 500. Find the profit or loss.

Solution :

C.P. of an article = Rs. 450  

S.P. of an article = Rs. 500  

S.P. is greater than C.P. so there is a profit.  

∴  Profit = S.P. – C.P.  

= 500 – 450 = Rs. 50.

Example :  A television set was bought for Rs. 10,500 and sold at Rs. 9,500. Find the profit or loss.

Solution :  

C.P. of the television set = Rs. 10,500  

S.P. of the television set = Rs. 9,500  

Here C.P. is greater than S.P. so there is a loss.  

Loss = C.P. – S.P.  

= 10,500 – 9,500 = Rs. 1,000. 

Case : Profit and Loss  successive profits and successive losses

When  two successive profits of x% and y% the net gain%  = [ x + y + { xy / 100 }]%.

When  two successive losses of x% and y% the net loss% = [ - x - y + { xy / 100 }]%.10)

When there is a gain of x% and a loss of y% the Net effect = [ x - y - { xy / 100}]%.

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Objective Profit and Loss Question 

1. 
   

   At what price must kantilal sell a mixture of 80 kg sugar at Rs. 6.75 per kg with 120 kg at Rs. 8 per kg to gain 20%?

1. A. Rs. 7.50 per kg     
2. B. Rs. 8.20 per kg      
3. C. Rs. 8.85 per kg      
4. D. Rs. 9 per kg        Correct Answer

2.  

   
   

   Bhajan Singh purchased 120 reams of paper at Rs. 80 per ream. He spent Rs. 280 on transportation. Paid octrai at the rate of 40 paise per ream and paid Rs. 72 to the coolie. If he wants to have a gain of 8 %. What must be the selling price per ream?

1. A. Rs. 86     
2. B. Rs. 87      
3. C. Rs. 89      
4. D. Rs. 90        Correct Answer

3.  

   
   

   Subhash purchased a tape recorder at 9/10th of its selling price and sold it at 8% more than its S.P. His gain is:

1. A. 8%     
2. B. 10%      
3. C. 18%      
4. D. 20%        Correct Answer

4.  

   
   

   I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?

1. A.  Rs.28     
2. B.  Rs.280        Correct Answer
3. C. Rs.140      
4. D.  Rs.70      

5.  

   
   

   A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?

1. A. Rs.370     
2. B. Rs.375        Correct Answer
3. C. Rs.350      
4. D. Rs.300      

6.  

   
   

   A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?

1. A. Rs.250       Correct Answer
2. B. Rs.225      
3. C. Rs.275      
4. D. Rs.200      

7.  

   
   

   If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?

1. A. 30%     
2. B. 33%      
3. C. 33 1/3%        Correct Answer
4. D. 35%      

8.  

   
   

   Oranges are bought at 11 for a rupee and an equal number more at 9 a rupee. If these are sold at 10 for a rupee, find the loss or gain percent?

1. A. 1% gain     
2. B. 2% gain      
3. C. 1% loss        Correct Answer
4. D. 2% loss      

9.  

   
   

   A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?

1. A. 75%     
2. B. 50%      
3. C. 100%        Correct Answer
4. D. 80%      

10.  

    
    

    At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?

1. A. Rs.62.50       Correct Answer
2. B. Rs.62.50      
3. C. Rs.75.00      
4. D. Rs.80.00      

11.  

    
    

    A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?

1. A. Rs.60000       Correct Answer
2. B. Rs.75000      
3. C. Rs.68400      
4. D. Rs.78400      

12.  

    
    

    A trader marked the price of the T.V. 30% above the cost price of the T.V. and gave the purchaser 10% discount on the marked price, thereby gaining Rs.340. Find the cost price of the T.V?

1. A. Rs.2250     
2. B. Rs.2000        Correct Answer
3. C. Rs.2150      
4. D. Rs.2200      

13.  

    
    

    A man buys milk at a certain rate per liter and after adding water to it sells the mixture at the same rate. Find in what ration he much mix water to milk so as to gain 20% on his outlay?

1. A. 1:5       Correct Answer
2. B. 1:20      
3. C. 2:5      
4. D. 1:6      

14.  

    
    

    A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?

1. A. Rs.600       Correct Answer
2. B. Rs.500      
3. C. Rs.250      
4. D. Rs.700      

15.  

    
    

    By selling an article at Rs.600, a profit of 25% is made. Find its cost price?

1. A. Rs.350     
2. B. Rs.400      
3. C. Rs.573      
4. D. Rs.480        Correct Answer

16.  

    
    

    By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?

1. A. Rs.600     
2. B. Rs.480        Correct Answer
3. C. Rs.500      
4. D. Rs.450      

17.  

    
    

    A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?

1. A. neither profit nor loss       Correct Answer
2. B. 1%      
3. C. 2%      
4. D. 3%      

18.  

    
    

    A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?

1. A. neither profit nor loss     
2. B. 3%      
3. C. 5%      
4. D. 4%        Correct Answer

19.  

    
    

    A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?

1. A. 20%     
2. B. 28%      
3. C. 33 1/3 %        Correct Answer
4. D. 35 2/7 %      

20.  

    
    

    A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?

1. A. 855 1/2 grams     
2. B. 833 1/3 grams        Correct Answer
3. C. 833 1/2 grams      
4. D. 875 2/7 grams      

21.  

    
    

    The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

1. A. 25     
2. B. 18      
3. C. 16        Correct Answer
4. D. 15      

22.  

    
    

    My friend collects antique stamps. She purchased two, but found that she needed to raise money urgently. So she sold them for Rs.8000 each. On one she made 20% and on the other she lost 20%. How much did she gain or lose in the entire transaction?

1. A. No loss/profit     
2. B. Rs.667 loss        Correct Answer
3. C. Rs.667 profit      
4. D. None of these      

23.  

    
    

    A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs.3150, Find at what price he must sell the first grade bicycles so that if he sells the second grade bicycles at three quarters of the price, he may make a profit of 40% on his outlay?

1. A. Rs.200     
2. B. Rs.240      
3. C. Rs.180        Correct Answer
4. D. Rs.210      

24.  

    
    

    A machine is sold at a profit of 10%. Had it been sold for Rs.40 less, there would have been a loss of 10%. What was the cost price?

1. A. Rs.175     
2. B. Rs.200        Correct Answer
3. C. Rs.225      
4. D. Rs.250      

25.  

    
    

    The initial profit percentage for a shirt is 87.5%, which is sold after giving a discount of 20%. Due to some reason the cost price of making a shirt increases by 25%. Now a shirt is sold after raising the marked price by Rs.500 and giving a discount of 25%. If the percentage profit still remains the same, find the new selling price of the shirt

1. A. Rs.800     
2. B. Rs.1,000      
3. C. Rs.1,200      
4. D. Rs.1,500        Correct Answer

26.  

    
    

    A property dealer sells a house for Rs.6,30,000 and in the bargain makes a profit of 5%. Had he sold it for Rs.5,00,000, then what percentage of loss or gain he would have made?

1. A. 15% loss     
2. B. 15% gain      
3. C. 16 2/3% gain      
4. D. 16 2/3 % loss        Correct Answer

27.  

    
    

    The evergreen shrubs at Ravi's nursery are planted in rows on a square plot of land measuring 2,401 square ft. The shrubs are planted in such a manner that the centres of the shrubs are 7 ft apart and the outer shrubs are planted along the edges of the plot, with a shrub at each corner. Ravi spent Rs.896 to cover all the costs necessary for raising this crop of the evergreen shrubs. If Ravi succeeds in selling each shrub for Rs.35, his profit will be what percentage of his total cost?

1. A. 100%     
2. B. 50%      
3. C. 125%      
4. D. 150%        Correct Answer

28.  

    
    

    A cash payment that will settle a bill for 250 chairs are Rs.50 per chair less 20% and 15% with a further discount of 5% on cash payment is

1. A. Rs.8075       Correct Answer
2. B. 7025      
3. C. Rs.8500      
4. D. None of these      

29.  

    
    

    Amit went to Mumbai and bought a pair of watches costing Rs.360 at 25% discount on each but on the way back he loses one of these watches and had to buy them (pair) again home. How much did he totally spend on the watches?

1. A. Rs.620     
2. B. Rs.720      
3. C. Rs.540        Correct Answer
4. D. Rs.630      

30.  

    
    

    The cost price of three varieties of apples namely A,B and C is Rs.20/kg, Rs.40/kg and Rs.50/kg. Find the selling price of one kg of apple in which these three varieties of apples are mixed in the ratio of 2:3:5 such that there is a net profit of 20%?

1. A. Rs.48     
2. B. Rs.48.6      
3. C. Rs.49.2        Correct Answer
4. D. Rs.49.8      

31.  

    
    

    On selling an article at successive discounts of 20% and 25%, a dealer makes a net profit of 20%. Find the net profit per cent if the dealer sells the same article at a discount of 25%.

1. A. 50%       Correct Answer
2. B. 40%      
3. C. 66.66%      
4. D. 60%      

32.  

    
    

    A book vendor sold a book at a loss of 10%. Had he sold it for Rs.108 more, he would have earned a profit of 10%. Find the cost price of the book.

1. A. Rs.432     
2. B. Rs.540        Correct Answer
3. C. Rs.648      
4. D. Rs.740      

33.  

    
    

    A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 g weight instead of 1 kilogram weight. Find his profit percentage.

1. A. 8%     
2. B. 12%      
3. C. 20%        Correct Answer
4. D. None of these      

34.  

    
    

    A man buys 6 dozen eggs for Rs.10.80, and 12 eggs are found rotten and the rest are sold at 5 eggs per rupee. Find his percentage gain or loss.

1. A. 11 1/9% gain     
2. B. 11 1/9% loss      
3. C. 9 1/11% gain      
4. D. 9 1/11% loss        Correct Answer

35.  

    
    

    By selling an article for Rs.144, a person gained such that the percentage gain equals the cost price of the article. The cost price of the article is

1. A. Rs.90     
2. B. Rs.80        Correct Answer
3. C. Rs.75      
4. D. Rs.60      

36.  

    
    

    Seems purchased an item for Rs.9600 and sold it for loss of 5 per cent. From that money she purchased another item and sold it for gain of 5 per cent. What is her overall gain/ loss?

1. A. Loss of Rs.36     
2. B. Profit of Rs.24      
3. C. Loss of Rs.54      
4. D. None of these        Correct Answer

37.  

    
    

    A farmer sold a cow and an ox for Rs.800 and got a profit of 20% on the cow and 25% on the ox. If he sells the cow and the ox for Rs.820 and gets a profit of 25% on the cow and 20% on the ox, the individual cost price of the cow and the ox is

1. A. Rs.515.60, Rs.115.60 (approx.)     
2. B. Rs.531.50, Rs.135.50 (approx.)      
3. C. Rs.530.60, Rs.131.60 (approx.)        Correct Answer
4. D. Cannot be determined      

38.  

    
    

    A trader purchases a watch and a wall clock for Rs.390. He sells them marking a profit of 10% on the watch and 15% on the wall clock. He earns a profit of Rs.51.50. The difference between the original prices of the wall clock and the watch is equal to

1. A. Rs.110       Correct Answer
2. B. Rs.100      
3. C. Rs.80      
4. D. Rs.120      

39.  

    
    

    What profit/loss per cent did Ravi earn if he purchased an item of Rs.5600 and sold it at three -fourths of its cost price?

1. A. Loss of 20 per cent     
2. B. Gain of 25 per cent      
3. C. Neither gain nor loss      
4. D. None of these        Correct Answer

40.  

    
    

    Even after reducing the marked price of a pen by Rs.32, a shopkeeper makes a profit of 15%. If the cost price be Rs.320, what percentage of profit does he make if he sells the pen at the marked price?

1. A. 25%       Correct Answer
2. B. 20%      
3. C. 10%      
4. D. 30%      

41.  

    
    

    The profit earned after selling an article for Rs.996 is the same as loss incurred after selling the article for Rs.894. What is the cost price of the article?

1. A. Rs.935     
2. B. 905      
3. C. Rs.945        Correct Answer
4. D. Rs.975      

42.  

    
    

    A shopkeeper marks the prices of his goods at 25% higher than the original price. After that, he allows a discount of 12%. What profit or loss did he get?

1. A. 15% profit     
2. B. 10% profit        Correct Answer
3. C. 10% loss      
4. D. 15% loss      

43.  

    
    

    A milkman buys milk contained in 10 vessels of equal size. If he sells his milk at Rs.5 a litre, he loses Rs.200; if he sells it at Rs.6 a litre, he would gain Rs.150 on the whole. Find the number of litres contained in each vessel

1. A. 20 L     
2. B. 30 L      
3. C. 25 L      
4. D. 35 L        Correct Answer

44.  

    
    

    A trader has 50 kg of rice, a part of which he sells at 10% profit and the rest at 5% loss. He gain 7% on the whole. How much was sold at 10% gain and how much was sold at 5% loss?

1. A. 40 kg and 15 kg     
2. B. 30 kg and 10 kg      
3. C. 35 kg and 40 kg      
4. D. 40 kg and 10 kg        Correct Answer

45.  

    
    

    Naresh purchased TV set of Rs.11250 after getting discount of 10% on the labeled price. He spent Rs.150 on transport and Rs.800 on installation. At what price should it be sold so that the profit earned would have been 15% if no discount was offered?

1. A. Rs.12937.50     
2. B. Rs.14030        Correct Answer
3. C. Rs.13450      
4. D. Rs.15467.50      

46.  

    
    

    A firm of readymade garments makes both men's and women's shirts. Its average profit is 6% of the sales. Its profit in men's shirts average 8% of the sales and women's shirts comprise 60% of the output. The average profit per shirt in women's shirts is

1. A. 0.0466       Correct Answer
2. B. 0.0666      
3. C. 0.0166      
4. D. None of these      

47.  

    
    

    A shopkeeper sells two radios at Rs.1540 each. On one he gains 12% and on the other he loses 12%. What was the net result of the sale of both the radios?

1. A. No loss no profit     
2. B. Gain of Rs.165      
3. C. Loss of Rs.45        Correct Answer
4. D. Gain of Rs.45      

48.  

    
    

    A loss of 19% gets converted into a profit of 17% when the selling price is increased by Rs.162. Find the cost price of the article.

1. A. Rs.450       Correct Answer
2. B. Rs.600      
3. C. Rs.360      
4. D. Rs.540      

49.  

    
    

    A machine is sold at a profit of 10%. Had it been sold for Rs.80 less, there would have been a loss of 10%. The cost price of the machine is

1. A. Rs.350     
2. B. Rs.400        Correct Answer
3. C. Rs.450      
4. D. Rs.520      

50.  

    
    

    The marked price for a pair of shoes is 60% above the cost price. A shopkeeper sells the pair of shoes after giving a discount of x%. Now he raises the marked price by x% and gives a discount of (x + 5)%. If the profit earned in the second case is twice that of the first case, find the value of x.

1. A. 20     
2. B. 25        Correct Answer
3. C. 10      
4. D. 15      

Problems on Average Questions with Solutions PDF

Basic Average Formula and Tricks

For Example : Find the average of all numbers between 5 and 49 which are divisible by 5. 

Solutions : Number are 5, 10, 15, 20, 25, 30, 35, 40, 45, These numbers are divided by 5.

Average Of numbers =	5+10+15+20+25+30+35+40+45	=	225
	9		9

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For Example : The average of 11 numbers is 30. If the average of first six numbers is 17.5 and that of last six is 42.5, then what is the sixth number? 

Solutions:   11 Number's Average is 30 [ Given ]

Sum of 11 Number's is 11 x 30 = 330

Average of first six numbers is 17.5 [ Given ] , so Sum of First 6 Number's is 17.5 x 6 = 105

Average of last six is 42.5 [ Given ] , so Sum of Last 6 Number's is 42.5 x 6 = 255

⇒ Sixth Number = ( Sum of First 6 Number's + Sum of Last 6 Number's ) - Sum of 11 Number's

⇒ Hence the Sixth Number is (105 + 255 ) - 330 = 30

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For Example : A person covers a distance of 50 km from P to Q at a speed of 30 km/hr and returns from Q to P at a speed of 40 km/hr. Find the average speed of person. 

Solutions:   Distance of 50 km from P to Q at a speed of 30 km/hr, Returns from Q to P at a speed of 40 km/hr 

Average Speed =	2 x 30 x 40	=	2400
	30 + 40		70

: : So the Average speed of the person = 34.28 km/hr

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  When new member is added or replaced by other member in the group.

 For Example : The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

Solutions:  Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

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Average formula for n natural number = (n + 1) / 2

Average formula of n even numbers = (n + 1)

If number value increase or decrease by X, then the average also increase or decrease by A.

In AP ( Arithmetic Progression ), if number of terms are

i) Odd – Average is the middle term.

ii) Even – Average is the average of two middle terms.

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Objective Question On Average Problem

1. The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography secured by him?

1. A. 40     
2. B. 50      
3. C. 60        Correct Answer
4. D. Data inadequate      

2.  

   
   

   A Mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Beans were written as 36 instead of 86 then find the correct average marks up to two decimal places.

1. A. 73.41     
2. B. 74.3      
3. C. 72.43      
4. D. 73.43        Correct Answer

3.  

   
   

   The average age of a husband and wife was 23 when they were married 5 years ago. The average age of the husband, the wife and a child who was born dining the interval, is 20 years now. How old is the child now?

1. A. 9 months     
2. B. 1 year      
3. C. 3 years      
4. D. 4 years        Correct Answer

4.  

   
   

   The average of four consecutive even numbers is one-fourth of the sum of these numbers. What is the difference between the first and the last number?

1. A. 4     
2. B. 6        Correct Answer
3. C. 2      
4. D. Cannot be determined      

5.  

   
   

   Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 15. What is the difference between the first and the third of the three numbers

1. A. 15       Correct Answer
2. B. 45      
3. C. 60      
4. D. None of these      

6.  

   
   

   The average of 25 results is 18, that of first 12 is 14 and of the last 12 is 17 Thirteenth result is

1. A. 72     
2. B. 78        Correct Answer
3. C. 85      
4. D. 28      

7.  

   
   

   Average age of seven persons in a group is 30 years. The average age of five persons of this group is 31 years.  What is the average age of the other two persons in the group?

1. A. 55 years       Correct Answer
2. B. 26 years      
3. C. 15 years      
4. D. None of these      

8.  

   
   

   Average weight of three boys P, T and R is 54(1/3) kg while the average weight of three boys T, F and G is 53 kg. What is the average weight of P, T, R, F and H

1. A. 53.8 kg     
2. B. 52.4 kg      
3. C. 53.2 kg      
4. D. Data inadequate         Correct Answer

9.  

   
   

   In a class of 52 students the number of boys is two less than the number of girls. Average weight of the boys is 42 kg, while the average weight of all the 52 students is 40 kg. Approximately what is the average weight of the girls?

1. A. 41 kg     
2. B. 29 kg      
3. C. 40 kg      
4. D. 38 Kg        Correct Answer

10.  

    
    

    While calculating the average of a batsman as 36 in 100 matches that he played, one of the score 90 was incorrectly noted as 40. The percentage error is

1. A. 0.6%     
2. B. 1.36%        Correct Answer
3. C. 1.34%      
4. D. 121%       

11.  

    
    

    The average sale of a car dealership was 15 cars per week. After a promotional scheme, the average sale increased to 21 car per week. The percentage increase in the sale of Car was 

1. A. 40%        Correct Answer
2. B. 140%       
3. C. 42(6/7)%      
4. D. 39.33%      

12.  

    
    

    In a class with a certain number of students, if one new student weighing 50 kg is added, then the average weight of the class increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original weight (in kg) of the class?

1. A. 46      
2. B. 42      
3. C. 27      
4. D. 47        Correct Answer

13.  

    
    

    The average marks of a student in 8 subjects are 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated, the average mark of the remaining subjects is 85. What is the highest mark obtained by him?

1. A. 94       Correct Answer
2. B. 91      
3. C. 89      
4. D. 96