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# Percentage Gain

Percentage gain means to express the profit or the gain in the form of percentages. This way makes it easier and faster for a person to understand the variables or the vitals of a business transaction. Sometimes it is useful to find the increase or decrease of an amount. It can also be useful to find the percentage increase or decrease, which is called profit and loss. In the following section, we will see what we mean by the Percentage Gain, we will state the formula for this and then proceed on to the application of this formula. Let us begin with a formal introduction to the topic.

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Calculating the profit or loss is all about calculating the change. In the profit and loss section, we have to understand that all of our calculations are based on the concepts of Selling Price, and Cost Price. The difference between the two determines if we have a situation of making a profit out of the transaction or will we just incur a loss. Other terms like the Marked Price, MRP and Discount are also very crucial and have been discussed in detail at other places. Let us recall these terms.

Cost Price: The price (amount) paid to purchase a product or the cost incurred in manufacturing a product is known as the cost price (CP) of that product.

Selling Price: The price at which a product sold is called selling price (SP) of the product.

Marked Price: The marked price or the mark-up price (MP) is the price that the shopkeeper/retailer fixes in the anticipation of some discount that they may be asked by a customer.

### Profit And Loss and Percentage

We can put the concept of profit and loss in the most simple words as follows: When SP < CP → Loss = CP – SP.

Similalry, when SP > CP → Profit = SP – CP.

## Percentage Loss and Percentage Gain Formula

Now, let us see how we calculate the percentage loss and the percentage gain.  Percentage Loss and Percentage Gain or Profit percentage both are calculated upon CP as follows:

Profit% = [Profit/CP] × 100

Loss% = [Loss/CP] × 100

Example 1: Suppose Company A produces 1000 T.V in the Year 2000 And 1200 T.V in the Year 2001. On the other hand Company, B produces 5000 T.V in the year 2000 and 5500 T.V in the year 2001. Which company has the better growth rate?

Answer: Look at company A. The increase is of 200 T.V and Company B the increase if of 500 T.V So in Numerical Sense Company B has Produced more than A. But we are not talking here about Numerical Growth. We are talking about the relative Growth. i.e Growth with respect to its previous year production. [Note: Like things are compared with like thing Only, Just Like you can’t compare Apple and Oranges]

Taking That Point Into Consideration, the Growth of Company A with respect to its Previous year
production will be (200/1000)×100 = 20%. And that for company B it will be (500/5000)×100 = 10%. So clearly Company A has a better growth rate than company B.

## Solved Examples For You

Example 2: Raman Purchased A watch for 1000rs and then Sold it to Nimesh for 1250 Rs. Calculate the Profit and Profit %?

A) 2%                    B) 12%                  C) 20%                       D) 25%

Answer: Most Simple Question which you will never get in Any Exam. But Basics are Basics we gotta revise it at least. So what happens here Raman purchases a Watch (You see word Purchase And You know it’s CP) at Rs. 1000. Hence, C.P = Rs. 1000.

And then he sells it at Rs. 1250 (You See the Word SELL Ok that’s our SP). So SP = Rs. 1250.

Now Profit, as I told, is nothing but SP – CP. So profit = Rs. 1250 – Rs. 1000 = Rs. 250. Now Profit % = [(Profit)/CP×100]. So profit % = [(250/1000)×100] = 25%. Therefore the correct option is D) 25%.

Example 3: Steve Sells an article for 1200Rs And he makes a profit of 20% in the Transaction. So What is the Cost price?

A) Rs. 500                  B) Rs. 1000                   C) Rs. 1500                     D) Rs. 2000

Answer: If you don’t know about something then assume it as x. So we take CP = x. Now If I sell an article at 20% profit then what will be our SP in terms of x?

x + 20%(x) = 1.2x [Because of percentage to decimal conversion. So 20% here is nothing but 0.2x and total SP will be x+ 0.2x = 1.2x. Remember add in case of the profit and subtract in
the case of loss].

And according to the Question he sold the article at Rs. 1200. So 1.2x = Rs. 1200 and we have x = Rs. 1000 which is our C.P. Therefore the correct option is B) Rs. 1000

Example 4: A man purchases 11 oranges for 10rs and Sells 10 oranges for 11rs.Find profit or loss%?

A) 12%                 B) 13%                   C) 31%                 D) 21%

Find the C.P of 1 orange that will be Rs. (10/11). Then find the S. P. of 1 orange that will be Rs. (11/10).

As it is clear that S.P. > C. P., hence the Profit will be SP – CP = 11/10 – 10/11 = (121 – 100)/110 = 21/110
Therefore the Profit % = [(profit)/CP]×100 = [(21/110)/(10/11)×100] = [(21×11)/(110×10)×100 = 21%. Hence the correct option is D) 21%.

Second – LCM method.
Take The LCM The two numbers present in the Question i.e LCM of 10 and 11 = 110. Now, this Is the number of oranges you will buy and sell and calculate the profit % on that. So CP of 110 Oranges = Rs. 100.

S.P of 110 Oranges = Rs. 121. Profit = Rs. 21. Profit% = 21% [calculated on the CP of 110 Oranges].

## Practice Problem:

Q 1: A man buys 8 pens for Rs 9 each. He sells 9 pens for Rs 8 each. Find the profit or loss percentage of the person?

A) 21% profit                     B) 12% loss                  C) 13% profit                 D) 21% loss

Ans: D) 21% loss

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