**Test links for this topic at the bottom of the page; scroll to the bottom of the page to take the tests.**

The world of Arithmetic is the world of practical maths. We see it all around: numbers, ratios, percentages floating all around us. In this same world, we have something known by the name of ‘Profit and Loss’. What is Profit and Loss? Well, go back to your childhood and recollect all those trips to the market where you used to work yourself up in a frenzy just to understand what the shopkeeper had done. You used every ounce of your mental strength to calculate prices, check totals and MRPs just to be sure that you were not cheated. That, my friend, was your first introduction with the world of Arithmetic: the world of cost-price, selling-price, mark-ups and discounts. We explore the very same world today, for your benefit.

As a starter, let us dig into the topic terminology.

**Profit and Loss Tooltip 1: The Definitions**

**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.

**Types of cost **

1. **Fixed cost** it is a type of cost which is fixed under all conditions and does not vary according to the number of units produced.

2. **Variable cost**: Variable cost is a type of cost which varies according to the number of units. This is pretty understandable.

3.** Semi-variable cost**: As the name suggests, these costs are the ones that are fixed in part and variable in part. Effectively, this is the case that we see most often.

Imagine the scenario in a factory. There is a capital cost, which remains the same under all conditions (fixed cost) and a variable cost of the product, which in turn depends upon various factors.

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

**Marked Price: **Head to a real-world scenario. Do shopkeepers put up price on the label that they wish to sell on or they put up an inflated price? If you think closely, majority of the shopkeepers mark-up their products, in anticipation of the discounts they would have to offer. This is a clever way of operating. Mark-up the price in advance, offer a discount and make the customer feel happy, and then sell the product. Pretty effective, eh?

**List Price: **List price or the tag price is the price that is printed on the tag of the article. For all practical purposes, we assume it to be same as the marked-price.

**Margin: **The profit percentage on selling price is known as MARGIN.

*Basic Problem 1: **Pranav sell an article at a discount of 80% and get a profit of 60% on that article calculate the mark up over the cost price? *

Let us put the above definitions in use.

Let us assume that Cost Price = Rs 100.

So, Selling Price = Rs 160.

Now, after giving a discount of 80% over MP, Rs 160 is the SP.

Let the Marked Price: MP

SP = 20% of MP

160 = 20% of MP

MP = 800

% Mark Up = (700/100) * 100 = 700 %.

*Things to remember in this question:*

*Mark Up over Cost Price = Marked Price – Cost Price = M*

*% Mark Up Cost Price = (M/CP) * 100*

*Mark Up over Selling Price = Marked Price – Cost Price = M*

*% Mark Up Selling Price = (M/SP) * 100*

*Focus closely on what is being asked. Remember Profit and Loss is nothing else but an application of Percentages and basic calculation skills. *

**Profit and Loss Tooltip 2: Absolute Basics**

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

2. One generates a loss when Selling Price < Cost Price.

3. Profit = Selling Price – Cost Price

% Profit = 100 * (Selling Price – Cost Price) / Cost Price

4. Loss = Cost Price – Selling Price

% Loss = 100 * (Cost Price – Selling Price) / Cost Price

**Profit and Loss Tooltip 3: Multiplying equivalents to figure out the sale price**

If there is a profit of P %,

Cost Price = C

Then

SP = {C*(100+P)} / 100

If there is a loss of L %,

Cost Price = C

Then

SP = {C*(100-L)} / 100

*Basic Problem 2: **Mehak and Pranav sells some article for Rs 8000 each. Mehak calculates her profit per cent on his CP and Pranav calculates his profit per cent wrongly on SP. What is the difference in their actual profit if both claim to have a profit of 60%? *

**For Mehak**

SP = Rs 8,000

Profit = 60% of CP

CP = Rs 5000

Profit = Rs 3000

**For Pranav**

SP = Rs 8,000

Profit = 60% of SP = 60% of 8000 = 4800

CP = Rs 3,200

Profit = Rs 4800

So, the difference in profit = Rs 1800

*Basic Problem 3: ** **Megha and Richa sold two articles at Rs 12,000 each. One is sold at a profit of 20% and another one at a loss of 20%. What is the net loss? *

For article-1

SP 1 = Rs 12,000

CP 1 = Rs 12,000/1.2 = Rs 10,000

For article-2

SP 2 = Rs 12,000

CP 2 = Rs 12,000/0.8 = Rs 15,000

So, total CP = Rs 25,000 and total SP = Rs 24,000

So, loss = Rs 1,000.

Hi, for the last example given(basic problem 3), could you provide an explanation of calculating the CP for each article? ( how is the SP being divided by 1.2 for article 1 and 0.8 for article 2)

Hi Bhavin

Let us take an another example to understand this

Consider the C.P. of article 1 = Rs. 1000

Now profit given = 20%

therefore the profit = Rs. 200

Therefore the S.P. = Rs. 1200(S.P. = (C.P. + profit)

Now S.P. = 1200 when C.P. = 1000

S.P. = 1 when C.P. = 1000/1200

S.P. = 12000 when C.P. = (1000/1200)x12000 = Rs. 10000

So the C.P. of the aritcle 1 = Rs. 10000

and if you see the 20% of 10000 is 2000

which means 10000+2000 = 12000.

Hence the cost of article 1 = Rs. 10000

Same you can calculate the C.P. of article 2

Thanks

Wordpandit