__Profit and Loss__

__Profit and Loss__

Today we will be covering **Profit and loss topic**, which is an important topic for competitive exams. **Profit and Loss**** Questions** are an important part of the QA section of most competitive exams like SBI, IBPS, PO/Clerk, LIC-AAO, SSC, etc. So it becomes relevant to know the right technique of solving these questions. Let us start with our topic **Profit and Loss**

__Introduction__

Before starting our topic let us take a quick revision of Percentage

**The percentage** is the method of expressing fractions or parts of ant quantity as a number out of 100. It is expressed in terms of hundredths

__What is the percent?__

The word percent means per hundred .thus, 31 percent means 31 part out of 100 parts, which can also be written as 31/100

The definition and utility of percentage can be made clear with the help of examples and further discussions in the articles

** Solution** Percentage of water in the mixture

**6/20*100=30%**

Shortcut to remember percentage into the form of reducing fraction we can just simply put the fraction instead by percentage to save our time for calculation.

To convert any fraction a/b to rate percentage, multiply it by 100 and put % sign. Alternatively to convert a rate percent to a fraction, divide it by 100 and remove the percentage sign.

Some important rules for the increment and decrement question we will study more on this topic later in the article.

Let us start with the basics of Profit and Loss concepts. Let us understand the common terminology for this topic.

__Profit and Loss Definitions__

**What is Cost Price(CP)?**

The amount paid for the purchase of the product or the cost in the manufacturing of a product is known as the cost price.

**Example** As we all know that we only purchase finished goods, not raw materials hence the finished goods are sold by factories to the retailer, retailers supply these goods to shops or markets. The price that retailers pay to factories is known as CP

**What are the types of costs?**

**1. Fixed cost:** the cost, which is always fixed under all circumstances and does not vary according to the number of units manufactured.

**2.Variable cost**: It is a type of cost, which varies according to the number of units manufactured. For example the price of gold crude oil, currency**.**

**What is the Selling Price?**

The price at which a product or an article is sold for is called the selling price (SP) of the product. Example: You purchase groceries from the supermarket. The price you paid to the supermarket will be SP

**What is Marked Price**?

Have you ever noticed shopkeepers put up price tags on the product that they wish to sell on or they put up an increased price? If you notice, the majority of the shopkeepers put their own tag for the products. Thet sometimes manipulate the rates for providing the discounts, they wan to offer. This is a clever way of making profit and marketing. In Marked Price, the offered discount price is included, this is to attract the customers with discounts and sell the products.

**What is List Price? (Tag Price)**

The tag price is the price that is mention on the tag of the product. We assume it the same as the marked-price.

**What is Margin?**

The profit percentage on the selling price of the product is known as MARGIN.

### Important formulae and shortcut tricks

The purpose of this blog is to create a basic approach to solve profit loss questions we will try to make it very simple for you and you can relate this topic to your daily life. Here we will discuss the concept, Formulas, Shortcuts, and Tricks that you can use to solve questions.

Let us start the topic

1. One can only earn a profit only if Selling Price> Cost Price

2. One can only suffer a loss when Selling Price < Cost Price.

3. Profit = SP – CP

Profit% will be calculated by = {(SP – CP)/ CP} *100

4. Loss = CP – SP

Loss%will be calculated by = {(CP – SP)/CP} * 100

5. Sale price:- If there is a profit of m %, Cost Price = CP

Then SP = {(100+m)/100}*CP

6. If there is a loss of n %, Cost Price = CP

Then SP = {(100-n)/100}*CP

7. Cost price:-

If there is a profit of m%,

Cost Price = CP

Selling price= SP

Then C = {100/(100+m)} x SP

suppose a loss of n %,

Then CP = {100/(100-n)}xSP

8. A dishonest shopkeeper claims to sell his goods at cost price, but he misleads customers by using a weight of lesser weight. Find his gain%.

9. A shopkeeper sells an item at a profit of m% and uses a weight which is n % less .find his total profit

10. When shopkeeper sells goods at loss on cost price but uses less weight.

11. A dishonest-shopkeeper sells goods at n%loss on cost price but uses A gram instead of B gram. Then his profit or loss percentage will be calculated by '-'

**Note:-** Profit or loss is decided according to sign.

** +ve = profit; –ve =loss.**

12. If the price of an item increased by r%, then the reduction in consumption of the item such that its expenditure remains the same will be calculated by

13. If the price of an item decreases by r% then the increase in consumption of the item, such that we have not to decrease expenditure on this item is

14. A reduction of x% in price on the product enables a person to buy y kg more products at the same price. Then the

15. Suppose there are two successive profits of m% and n% on any product such that the net percentage profit will be calculated by=[m+n+mn/100]

When there is a profit of m% and loss of n%,

then net percentage profit or loss = [m – n – mn/100]

Note: Profit or loss will be decided according to sign.

** +ve = profit–ve =loss**.

16. When each of the two things is sold at the same price, and a profit of P% is made on the Object1 and a loss of L% is made on the Object2, then the percentage gain or loss will be.

Few problems are based on the topic of the population hence it is important to remember to some short tricks methods to solve any problems within minutes

__Basic approach__

**Example 1: Ashwin sells a TV at a discount of 80% and he gains 60% on that TV. Calculate the market price over the cost price?**

Solution

Let the CP of the TV be Rs 100.

then the SP of the TV will be Rs 160.

Now, According to the question, Discount of 80% over TV MP, Rs 160 is the SP.

Let the Marked Price be MP

SP = 20% of MP

160 = 20% of MP

160=20/100*MP

On calculating

MP = RS 800

Mark Up percentage = (700/100) × 100 = 700 %.

**Important notes to solve these types of question:**

Mark Up over the Cost Price =MP–CP= x

% Mark Up Cost Price = [{x/CP} x 100]

Mark Up over the Selling Price = Marked Price – Selling Price = y

% Mark Up Selling Price = [{y/SP} x 100]

Profit and Loss is not a typical concept it is just a simple application of Percentages and it requires some basic calculation skills.

**Equivalent for Sale Price:**

If there is a Gain of P % is made on the article then SP Will be calculated by

Then, SP = {(100+P)/100} x CP

If there is a Loss of L %is made on the article then SP Will be calculated by

Then SP = {(100-L)/100} x CP

Where SP=Selling Price, CP=Cost price, L=Loss, P=profit

**Equivalent for Cost Price:**

If there is a Gain of P %, is made on the article then CP Will be calculated by

CP = [{100/(100+P)} x SP]

If there is a loss of L %, is madeon the article then SP Will be calculate by

Then

CP =[{100/(100+L)} x SP]

Where SP=Selling Price, CP=Cost price, L=Loss, P=profit

**Example-1: Neha and shubham sells some article for Rs 8000 each. Neha calculates her gain percent on her CP and Shubham calculates his gain percent wrongly onSP. What is the difference of their actual gain if both claim to have a gain of 60%?**

Solution:

For Neha

SP = Rs 8,000

gain = 60% of CP

CP = Rs 5000

gain = Rs 3000

For Shubham

SP = Rs 8,000

gain = 60% of SP = 60% of 8000 = 4800

CP = Rs 3,200

gain= Rs 4800

So, the difference in gain = Rs 1800

**Example-2: Nikhil and Harshita sold two articles at Rs 12,000 each. One is sold at a profit of 20% and while harshita sold her article at a loss of 20%. What is the overall loss?**

Solution:

**For article**-1

SP 1 = Rs 12,000

CP1 = Rs 12,000/1.2 = Rs 10,000

**For article-2**

SP2 = Rs 12,000

CP2 = Rs 12,000/0.8 = Rs 15,000

So, Total CP = Rs 10,000+Rs 15,000=Rs 25,000

Total SP =Rs 12,000+Rs 12,000= Rs 24,000

So, overall loss = Rs 1,000.

**What are Discounts?**

Now let us discuss the Discount because it is also an important part of Profit and loss

**Discounts** are offered in the article is always on the marked price and the selling price is calculated by reducing discount offered on the marked price.

For making it easier for you let us consider some examples, let us assume:

D% = Discount

CP = Cost price

MP = Market price

SP= Selling price

G% = Gain Percentage

Now**,**

Discount = % of marked price, MP

Discount = (MP) – (SP) Where MP Marked Price, SP=Selling Price

Marked Price –Discounted Amount = Selling Price

M (1-x%) = Selling PriceAlso, SellingPrice = CP+Gain

Thus,

MP (1 – Discount %) = CP (1 + Gain %)

__Profit and Loss: Concept of successive discounts__

If successive discounts of **a%** and **b%** are allowed on the marked price of an article of the discount then, after discount the Selling Price of the article will be calculated by

**SellingPrice** = **(1-a %)( 1-b %)x MP**

__SOME SOLVED EXAMPLE__

__SOME SOLVED EXAMPLE__

__Example-1:__** Aakansha offers her customers a reduction of 100 percent on her beauty merchandise product and if she still makes a profit of two hundredths. What is the particular value to her of that beauty product marked Rs 4000?**

**Solution:
Marked price** = Rs. 4000

**Discount**= 10%

**Profit**= 20%

Therefore, the Selling Pricebeauty merchandise = 90% of 4000

Therefore, 400 x 90/100 = Rs. 3600

**Sellingprice**= Rs. 3600

**Profit**= 20%

**Costprice**

**beauty merchandise**= 100/120 x 3600 = Rs 3000

**Example-2: Ravi offers a 10% discount on his shop and he offers a further discount of 5% on the reduced price for those customers who pay via DEBIT/CREDIT Card. What does a customer have to pay in the card for speakers of Rs.2000?
Solution:**

Price of the Speakers= Rs 2000

After a Discount of 10% Marked price would be Rs. 1800

Since he is purchasing the Speakers by card, so a discount of 5% is applicable again on the reduced marked price. Thus, the final selling price the Speakers would be of

**Rs. 1710**

__Profit and Loss: Basic Question types__

__Profit and Loss: Basic Question types__

**Type-1: Comparing quantities of goods and prices**

In these types of questions, Cost Price of an article is compared with the SP of an article. In this, both are equated with each other. Let us see an example:

**Example-3: The cost price of 40 Pens is equal to the selling price of 50 Pens. Calculate the profit or loss percentage?**

**Solution**:

According to the question

Cost Price of 30 Pen = Selling Price of 40 Pen

CP/SP = 40/50 =4/5

1 – CP/SP = 1- 4/5= 1/5

So, Loss percentage will be calculated by

= (1 – CP/SP) x 100 = 1/5x 100 = 20%

SHORT CUT TRICK

We can also solve this type of question by the following method

CP of 40 Pen = SP of 50 Pen = Rs 120 (Suppose)

So, CP of one Pen= Rs4, SP of one Pen = Rs5

Obviously, there is a loss of Re 1 Loss percentage = 1/5 X 100 = 20%

For the free online quiz on Profit and loss, click here

Author: Ashwani Kumar

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