# Profit and Loss

## Introduction

Profit and loss is an important topic of the arithmetic section of quantitative aptitude. Profit and loss is calculated on the cost price. The price at which a trader buys an article is called the Cost Price and the price at which a trader sells an article is called the selling price. Let’s see some more terms related to profit and loss:-

Profit: If the selling price of an item is more than its cost price, then there is a profit/gain on that item. i.e

SP - CP = Profit/Gain.

Loss: If the cost price of an item is more than its selling price, then there is a loss on that item. i.e

CP -SP = Loss

Marked Price: The price marked on the article in shops is called the Marked Price of that article, abbreviated as M.P.

Discount: Discount is the amount given on the marked price by lowering the price. S.P = M.P – Discount Or,

Discount = M.P – S.P

Remember that whenever you want to calculate profit or loss, it will always be calculated on cost price, but when it comes to calculating discount, it will always be calculated on the marked price.

Now let’s discuss some shortcuts that will take you to answers within seconds:

Trick #1: If m% and n% are two consecutive discounts on a scale, then the equivalent single discount will be (m+n-mn/100)%.

Nice shortcut. Isn’t it?

Trick #2: Suppose you are given the marked price and want to calculate the selling price, then one way is to do the whole calculation, however there is a shortcut: S.P = M.P * [(100-rate of discount)/100]

Yes, That simple it is!

Trick #3: Suppose you have the Selling price with you while solving a question, and you want to find a marked price; then, another quick formula that would help us:

M.P = (100*S.P)/(100 - rate of discount)

Now, let’s discuss some basic formulas for calculating profit and loss:-

## Basic Formulas Related to Profit and Loss

1. Profit = SP – CP                                     6. Loss = CP – SP

2. SP = Profit + CP                                     7. SP = CP – Loss

3. CP = SP – Profit                                     8. CP = SP + Loss

4. Percentage Profit = (Profit/CP)×100      9. Loss% = (Loss/CP) ×100

5. SP = CP + Gain

= CP + (Gain%/100) × CP

= (1 + Gain%/100 ) × CP

## Problems

Now let’s see some questions based on the above formulas:

Ques 1. You bought an item of 800 Rs and you sold the item at a profit of 10%. What are the selling prices and absolute profit?

Ans 1. Cost price is given as, CP = 800 Rs

% profit = 15. 15% of 800 = 800×15/100 = 120.

Hence SP = 920 Rs.

So the absolute profit will be 920 - 800 = 120Rs.

Now, let’s see a problem based on markup price and discount:-

Ques 2.  The cost price of an article was 800 and it is sold at a discount of 10% and at a profit of 12.5%. What is the selling price and mark price?

Ans 2. Given:-

CP = 800

%Profit = 12.5,

We know,

SP = CP + CP×% Profit

SP = 800 + 800×12.5/100 = 900.

Let Marked price be x

Discount = 10%

SP = MP - MP×Discount%

SP = x - x×10/100 = 0.9x and we have SP = 900. Hence 900 = 0.9x , x = 1000.

Ques 3. A man sells 2 items 1 at a profit of 20% and the other at a loss of 20% and the SP of both the items are equal. What is his % profit or loss?

Ans 3. If a man sells two items at the same price in which he sells one at a profit of x% and the other one at a loss of x%, then the result will always be a loss percent of [x/10]^2 %

Here x is given as 20. After putting these values in the formula the answer will be (20/10)^2 = 4% Loss

Ques 4. A shopkeeper wants to mark the price of an article such that by offering a 5% discount, he is able to get 33 % profit. Find the percent of CP above which the article should be marked?

Ans 4. Let the cost price of the article be Rs. 100

=> Selling price of the article = Rs. 100 + 33% of CP = Rs. 133

Let the marked price be Rs. M

=> Selling price = Marked Price – Discount

=> 133 = M – 0.05 M

=> 133 = 0.95 M

=> M = 140

=> M – CP = 140 – 100 = 40

Therefore, percent of CP above which the article should be marked = (40 / 100) x 100 = 40 %

Ques 5. By selling an article at Rs. 800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?

Ans 5. It is given that S.P = 800 and profit percent is given as 25%.

Now CP  = (SP)*[100/(100+p)]

= 800 * [100/125] = 640
Loss = 25%

= 25% of 640 = Rs. 160
SP = CP - Loss

= 640 - 160 = Rs. 480

Ques 6. Profit after selling a notebook for Rs. 425 is the same as loss after selling it for Rs.355. The cost of the notebook is?

Ans 6. Let the Cost price be Rs. x.

It is given that,

Profit = Loss
425 – X = X – 355 (or)
2X = 780 or X = 390

X = 390.

Hence the cost of the notebook will be rs 390.

Ques 7. A shopkeeper bought 150 books at the rate of Rs. 500 per book. He spent Rs. 500 on transportation and packing. If the marked price of the book is Rs. 520 per book and the shopkeeper gives a discount of 5% on the marked price then what will be the percentage profit gained by the shopkeeper?

Ans 7. The cost price, i.e C.P. of 150 books  = 150 * 500 = Rs. 75000

Including the transportation and packing charges,
∴ Total C.P. = 75000 + 500 = Rs. 75500
Marked price of 150 books = 150 * 570 = Rs. 82500
Selling price after discount = 82500 * 95 / 100 = Rs. 78375
∴ percentage profit = [(78375 – 75500) / 75500] * 100 = 3.8%

Hence the percentage of profit gained by shopkeepers is 3.8.

## Key Takeaways:

So you can see that questions on profit and loss will be arriving around a few formulas that I have discussed in this blog. So be thorough with these shortcuts and formulas, and you will be able to solve almost all questions you will be getting in your aptitude tests.

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