Thursday, 27 April 2017

Profit and Loss Problems I- Profit and Loss Formulas

Every competitive exam has profit and loss on its syllabus and the question papers have questions on it without fault. Read on to find out what is profit and loss and for a complete list of profit and loss formulas.

Profit and Loss Formulas
There is no escaping from profit and loss if you are appearing for SBI PO, IBPS and SSC CGL Exam. But if you are someone who skips a problem, just because it is from profit and loss then this 2 blog series on profit and loss is an answer to your woes. We will start with discussing from the very basic- what is profit and loss and the entire list of profit and loss formulas. If you want to understand what is profit and loss, it is important that you study percentages before this, because profit and loss is primarily based on percentages.
Profit and Loss Formulas

What is Profit and Loss?

 Profit and loss is a part of basic mathematics that deals with the transactions where money is involved. Whenever an article is sold or purchased, there are commercials involved. Sometimes there is a profit, sometimes a loss and in other cases neither of the two. This difference is calculated and then converted to percentage to make comparison easier.
Let’s take a scenario where you go to a shop and buy an article. For you to buy the article from the shopkeeper, the shopkeeper should posses it either by buying it from some other source or by manufacturing it. In either of these cases he spends money in procuring it and this is the cost price of the article. The shopkeeper then sells the article to you, and the price at which you buy it is called the selling price. If the shopkeeper sold the article to you at a price higher than the price at which he acquired it, he made a profit. If he sold it to you at a price lower than that, he made a loss.

Important Terms for Profit and Loss Formulas-

Before we move ahead to the list of important profit and loss formulas, we need to discuss some important terms that constitutes these profit and loss formulas.

Cost Price (CP) - The price at which an article is purchased by the seller is called the Cost Price of the article.

Selling Price (SP) - The price at which an article is sold is called its Selling Price.

Profit or Gain (P) - The difference between SP and C.P if it is positive, that amount is called Profit or Gain. If the selling price of the article is more than its cost price, then the seller makes a profit.

Loss- The difference between CP and SP if it is positive, that amount is called Loss. If the selling price of the article is less than the cost price of the article, then the seller makes suffers a loss on it.

Note that for all terms that base or point of reference is always Cost Price.

Why is Profit and Loss Calculated in Percentage?

As we will move to the next section, you will notice that all profit and loss formulas deal with percentage this is because percentage makes comparison easier. Imagine that there are two shopkeepers ‘A’ and ‘B’- they make a profit of Rs.10 and Rs.100 respectively, however it would be very unfair to compare the two without knowing the cost price of their articles or the investment made. Now let’s add the additional information, the selling cost price of the article sold by ‘A’ and ‘B’ respectively was of Rs.10 and Rs.4000. Now if you compare, a profit of Rs.10 on an article of Rs.10 is way better than a profit of Rs.100 and Rs.4000. Therefore profit and loss is calculated in percentage and for this we always consider CP as 100% and SP as 100% plus profit% or 100% minus loss%.


List of Profit and Loss Formulas-

Profit and Loss Formulas

Simple Problems based on Profit and Formula-

Now it’s time to discuss some basic profit and loss problems that can be answered using profit and loss formulas.
Problem 1: A shopkeeper bought an article for Rs.400 sold it for Rs.500, what is his profit or loss percentage on this transaction?

Solution 1:
On reading this question we know that CP of the article is Rs.400 and SP of the article is Rs.500, from this we also come to the conclusion that the shopkeeper has made a profit on this transaction as SP > CP. The formulas to be used from the list of profit and loss formulas is –
Profit and Loss Formulas
Step 1
Substituting the values in the appropriate formulas for the list of profit and loss formulas, we get-
Profit % = [(500-400) x 100] / 400
Profit % = [100 x 100] / 400
Profit % = 25%

Therefore the profit made by the shopkeeper on this transition is 25%

Problem 2: An umbrella was sold at a profit of 20%. What is the selling price of the umbrella if the shopkeeper procured it at a cost of Rs180/- ?

Solution 2:  
We can you the formula below from the list of profit and loss formulas to get the answer to this question-
Profit and Loss Formulas
Step 1
Substituting values in the formula above be get-
Selling Price = [(100 + 20) / 100] x 180
Selling Price = 12 x 18
Selling Price = 216

Therefore the selling price of this umbrella is Rs.216

Alternate Solution for Problem 2:  
Another way to solve the same problem, without profit and loss formulas, can be by using the concept of percentages. We know that CP is always 100%,
Step 1
We can say from this that
100% of CP = 180

Step 2
When the profit is 20%, SP will be 20% more than CP
SP = 120% and we have to find this value

Step 3
From above we can say
SP = (120 x 180) / 100
SP = 216

Therefore the SP of the article is 216.

Problem 3: An article was sold for Rs.13,000 at a loss of 35%. What is the Cost Price of the article?

Solution 3:  
We can easily solve this question by replacing values in the appropriate formula for the list of profit and loss formulas –
Profit and Loss Formulas
Step 1
Replacing values in the above formula, we get
CP = [100/ (100 – 35)] x 13000
CP = (100/ 65) x 13000
CP = 20,000

Therefore CP is Rs.20,000.

Alternate Solution for Problem 3:  
Another way to solve the same problem, without profit and loss formulas, can be by using the concept of percentages, just like the previous problem. We know that CP is always 100%,

Step 1
We know if the CP is 100%, with 35% loss,
SP = 100% – 35% = 65%
We also know that this 65% is actually 13,000

Step 2
By Cross Multiplication we can solve this, we get-
CP = (100 x 13000) / 65
CP = 20,000

Therefore CP is Rs.20,000.

Practice Profit and Loss Problems based on Profit and Loss Formulas

Question 1: Naresh purchased a TV set for ` 11,250 after getting a discount of 10% on the labeled price. He spent ` 150 on transport and ` 800 on installation. At what price should it be sold so that the profit earned would be 15%?
1) ` 12,937.50      2) ` 14,030      3) ` 13,450       4) ` 15,467.50       5) None of these

Question 2: Manoj sold an article for ` 15,000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%? What is the cost price?
1) ` 12,500      2) ` 13,500      3) ` 12,250      4) ` 13,250      5) None of these

Question 3: If Ramu buys books at 11 books for ` 10 and sells at 10 books for ` 12, then what will be his gain percent?
1) 11%      2) 22%      3) 32%      4) 15%      5) None of these

Remember to leave your answers in the comment section below!

And don’t forget to keep practicing.
Profit and Loss Formulas


Whatsapp Share Share on whatsapp

0 comments:

Post a Comment