PROFIT AND LOSS




About the topic profit and loss

Profit and loss play a major role in quantitative aptitude test. It is bit difficult to score marks in competitive exams without knowing the shortcuts related to time and distance.  We might have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

Points to Remember

COST PRICE (C.P):
                  The amount paid or expenditure incurred in purchasing or producing an object is known as its cost price
SELLING PRICE (C.P):
                  The price it which a person a product is called selling price.
MARKED PRICE or LIST PRICE (M.P):
                   It is the price marked on the product or indicated in the price list. It is the price at which the product is intended to be sold. It is the price which is above the cost price and increased value on the cost price is called markup.
PROFIT = S.P - C.P
PROFIT PERCENTAGE = (Profit/C.P)X100%
LOSS = C.P - S.P
LOSS PERCENTAGE = (Loss/C.P)X100%
MARGINAL PRICE = Cost Price + Markup value
SELLING PRICE = Marked Price - Discount
DISCOUNT = Marginal price - Selling price
DISCOUNT PERCENTAGE = (Discount value/M.P)X100%
Let "x" be the C.P of a product and "P" be the profit percentage

Then S.P = (100+P)% of C.P
Let "x" be the C.P of a product and "P" be the loss percentage

Then S.P = (100-P)% of C.P
SHOP KEEPER USING FALSE WEIGHT:
                  A trader cheats his customer to make a profit by stating that he sells at cost price.But he gives his customer less than 1000 grams (false weight) for every kg.

Cheated Value = Original Weight - False Weight

Profit Percentage = (Cheated Value/False Weight)X100%
When two articles are sold at the same price such that there is a profit of P% on one article and a loss of P% on the other.Then irrespective of what the actual selling price is, the net result of the transaction is loss.

The loss percentage = P2/100
When the cost price of two articles is same such that there is a profit of P% on one article and a loss of P% on the other.Then irrespective of what the actual selling price is, the net result of the transaction is no profit no loss.

Why is this topic needed?

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today it is bit difficult to score marks in competitive exams without knowing profit and loss shortcuts. Whether a person is going to write placement exam to get placed or a student is going to write a competitive exam in order to get admission in university, they must be profit and loss shortcuts. This is the reason for why people must study this topic.

What is the advantage of this topic?

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

How can students know profit  and loss shortcuts?

Students will learn, how and when they have to apply shortcuts to solve the profit and loss problems which are related to profit and loss. Apart from the regular shortcuts, students can learn some additional tricks in this topic profit and loss problems. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to solve the problems which are being asked from the topic profit and loss in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time. 

Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve profit and loss problems. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some profit and loss problems such that how loss shortcuts can be used. You can check your answer online and see step by step solution.

1. A trader cheats his customer to make a profit by stating that he sells at cost price but gives his customers only 800 grams. for every 1000 grams. What is his profit percentage? 

               (A) 24%                             (B) 25%
               (C) 26%                             (D) 27%

jQuery UI Dialog functionality
The trader delivers only 800 grams to his customer while declared it as 1000 grams and collects the cost price of 1000 grams.

Profit Percentage = (Cheated Value/False Weight)X100%
Here, cheated value = 200, false weight = 800
Profit Percentage = (200/800)X100% = 25%

Hence, the profit percentage is 25%

2. A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $ 1656 for it. What is the price at which A bought the item?

               (A) $ 1200                     (B) $ 1210
               (C) $ 1220                     (D) $ 1230

jQuery UI Dialog functionality
Let "x" be the cost price of A

B's cost price = A's selling price
B's cost price = 115% of x = 1.15x

C's cost price = B's selling price
C's cost price = 120% of 1.15x = 1.2(1.15x) = 1.38x
C's cost price = 1.38x

[Note : Let "x" be the C.P of a product and "P" be the profit percentage, then S.P = (100+P)% of C.P]

But C's cost price = $1656 (given)

So, 1.38x = 1656 ===> x = 1656/1.38 = 1200

Hence, the price at which A bought the item is $ 1200

3. Mr. Lenin sold a chair at a loss of 15%. If he had sold at a profit of 10%, he would have got $100 more. What is the cost is the cost price of the chair?   

               (A) $ 370                     (B) $ 380
               (C) $ 390                     (D) $ 400

jQuery UI Dialog functionality
Let "x" be the cost price of the chair

When the chair is sold at a loss of 15%, S.P = 85% of x = 0.85x

When the chair is sold at a profit of 10%, S.P = 110% of x = 1.1x

From this given information, when the chair is sold at 1.1x, he receives $100 more than when it is sold at 0.85x

Difference between 1.1x and 0.85x = 100
1.1x - 0.85x = 100 ===> 0.25x = 100 ===> x = 100/0.25 = 400

Hence, the cost price of the chair is $400.

4. If good are purchased for $ 1500 and one fifth of them sold at a loss of 15%. Then at what profit percentage should the rest be sold to obtain a profit of 15%? 

               (A) $ 370                     (B) $ 380
               (C) $ 390                     (D) $ 400

jQuery UI Dialog functionality
C.P of (1/5)th of goods = 1500/5 = 300

Loss at 15% on $ 300 = (15/100)X300 = 45

As per the question, we have to get 15% profit on 1500.

15% profit on 1500 = (15/100)X1500 = 225.
Already we got loss $45.

When the remaining (4/5)th of goods ($1200) is sold, the amount gained to be $ 270 (225+45=270) in order to obtain the overall profit of 15%.

Required percentage = (270/1200)X100 = 22.5%

Hence to obtain a 15% of profit, the rest to be sold at a profit of 22.5%

5. John scored 35% marks in an examination but failed by 35 marks. Find the maximum marks, if the pass mark is 40%. 

               (A) 500                     (B) 700
               (C) 700                     (D) 400

jQuery UI Dialog functionality
Let "x" be the maximum mark.

Then, pass mark = 40% of x = 0.4x ----(1)
John scored 35% marks and failed by 35 marks. If he had scored another 35 marks, he would have passed.

From this, pass mark = 0.35x + 35 ----(2)

From (1) and (2), we get
0.4x = 0.35x + 35 ===> 0.05x = 35 ===> x = 700

Hence, the maximum marks is 700

6. By selling 20 articles, a trader gained the selling price of 5 articles. Find the profit percent.  

               (A) 32.33%                     (B) 33.33%
               (C) 34.33%                     (D) 35.33%

jQuery UI Accordion - Default functionality
Let "x" be the selling price of 5 articles. Then, profit = x

If S.P of 5 articles is "x", S.P of 20 articles = 4x (Because 20 = 4X5)
C.P of 20 articles = S.P of 20 articles - Profit
C.P of 20 articles = 4x - x = 3x
Then, C.P of 20 articles = 3x and profit = x

Profit Percentage = (x/3x)X100% = (1/3)X100% = 33.33%

Hence, the profit percentage is 33.33%

More Quantitative Aptitude Topics

1. Problems on Numbers

2. HCF and LCM Problems

3. HCF and LCM Word Problems

4. LCM and HCF Calculator

5. Problems on Trains

6. Time and Work problems

7. Time and Distance Problems

8. Problems on Ages

9. Problems on Average

10. Problems on Boats and Streams

11. Problems on Ratio and Proportion

12. Allegation and mixture

13. Percentage word problems

14. Problems on Partnership

15. Simple Interest Problems

16. Compound Interest Problems

17. Permutation and Combination Problems

18. Calendar Problems

19. Formulas for shapes

20. Mensuration

21. Clock Problems

22. Word Problems on Simple Equations

23. Word Problems on Simultaneous Equations

24. Problems on Quadratic Equations

25. Word Problems on Quadratic equations

26. Pipes and Cisterns Shortcuts

27. Surds and Indices




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