Quant Study Notes & tricks to solve Profit & Loss questions

Profit & Loss:

Cost Price-The price at which an article is purchased is called its cost price (C.P.)

Selling Price-The price at which the article is sold is called its selling price (S.P.)

CP = Cost Price = The price at which an object is Purchased

SP = Selling Price = The price at which the object is Sold.

When SP < CP → Loss = CP - SP

When SP > CP → Profit = SP - CP

Note: Loss% and Profit% both are calculated upon CP

Profit% = [Profit/CP] * 100

Loss% = [Loss/CP] * 100

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

Now 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 relative Growth. i.e Growth with respect to it's previous year production. [ 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 it's 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.

Cost Price aka CP 

In my methods I Consider CP to be an Absolute Value of 100%. So if anybody Says he made profit of 20% it means He sells the Object at 120% or C.P 100% and Profit is 20% then it means SP = 1.2x( It will be more clear to you when i will explain Different Case)

Profit or Loss both are calculated with respect to C.P i.e CP is Always used as a base while calculating profit and loss.

Selling Price aka SP

I think by Common Sense you all know that If SP>CP then you will have profit whose value will be (SP - CP) In terms Of numerical Value.

And Profit % will be [(SP-CP)/CP] * 100 or [(Profit/CP)*100] [ remember i told you that profit and loss both are calculated on CP i.e taking CP as Base, So all you have to do is calculate Profit in terms of numerical value( SP - CP) and then divide it by the base(CP) and then multiply it by 100 and you will get your profit %]

Eg. CP of a pen is 10 Rs and SP is 12 Rs. What is profit and profit % ?

Pretty easy Huh !! Just calculate profit first So it will be SP - CP = 12-10 = 2RS

And profit % [(SP-CP)/CP]*100 = [(12-10)/10]*100 = [(2/10)*100] = 20%

So now I think The difference between profit and profit % is clear to you.

Now If you know What is Profit then you all must know That what is Loss and when loss Occurs.

Loss occurs when we make some pretty bad decisions and We go out Nuts and Start selling The object at a rate less than the purchasing price of the object.

Lets Put that in Mathematical Way. If CP>SP then there is a case of loss. to Find out the amount of loss all you have to do is (CP - SP)

And to calculate Loss% nothing difficult just the usual stuff [(CP-SP)/CP*100] or [(Loss)/CP*100] [ Look again I told you both Loss and profit are calculated taking CP as Base. So what i have done in the formula is That i calculated Numerical Loss and then divided it by our BASE i.e CP and Then Multiplies it by 100 To get our Loss%]

And i don't think I have to explain again the difference between loss and Loss %. 

So now Moving On to Other basic Stuff.

Marked Price aka MP= The Price at which a Product is Marked[ Like when you go to Your Local Market for buying Some nice Sunglasses( I mean fake RAY BAN's ;) ) And the Dealer say the cost is 1000rs and It's Also Marked on the Box but as we all know that it's just a MARKED PRICE and he will eventually sell that Ray Ban to you at 200Rs, And well if you are good at Bargaining then he will even sell it you at 100RS, And If It's me He will give it ME for free and even pay me 50RS back :P Well just Joking :P So that is our Marked Price] 

Discount % = It's like concession on the MARKED PRICE. The dealer says I Am just giving You a discount Man You are a regular customer and blah blah blah And you are like my relative and all the BS( But here is the catch The Discount % is always calculated on M.P In the above example of RAY BAN if you want to calculate the Discount % then It's Easy The MP was 1000Rs he Finally Sells you that Ray Ban at 200 So discount Given = MP - SP i.e 1000-200 = 800rs 

Now Discount % is calculated taking MP as BASE so Discount % will be 

[(MP-SP)/MP]*100 = [(1000-200)/1000]*100 = 80%]

Discount is calculated on MP but Marking of MP is done with respect to CP.

For example if I say I bought Something for 500rs and I marked the Product 60% above the CP then It means I marked the product 60% of 500 = 300 above CP means 500+300 = 800rs. OK 

CASE 1- Simple Profit and Profit % Calculation

Mohit Purchased A watch for 1000rs and then Sold it to  Nimesh for 1250rs. Calculate the Profit and Profit %?

Most Simple Question Which You will never get in Any Exam :P( But Basics are Basics we gotta revise it at least)

So What happens here Mohit  purchases a Watch( You see word Purchase And You know it's CP) at 1000rs 

SO C.P = 1000rs

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

So SP = 1250Rs

Now Profit as I told is nothing but SP - CP So profit = 1250-1000 = 250rs

Now Profit % = [(Profit)/CP*100] So profit % = [(250/1000)*100] = 25%

CASE - 2

Now The Watch That Nimesh purchased for 1250rs Is Sold Again by Her at Rs 625. So what will be Loss and Loss %

Again Usual Stuff

Loss = CP - SP

Loss = 1250 -625 = 625

Loss% = [(loss/CP)*100] = [(625/125)*100] = 50%

So we have a 50% loss here.

Case 3 Inversion case

Profit or loss% is Give and CP or SP is Given and you have to find SP or CP

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

I told You once 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 ?

yeah it's pretty simple 1.2x [ Because is told you percentage to decimal conersion So 20% here is nothing but 0.2x and total SP will be x+ 0.2x = 1.2x remember add in case of profit and subtract in case of loss]

And according to the Question he sold the article at 1200rs

So 1.2x = 1200rs 

So x = 1000Rs.

Steve  again sells an article for 1200rs but this time he suffers a loss of 20%. What will be the C.P?

Now just Take CP = x

So as i Told S.P will be ? yeah 0.8x ( As i said add in case of profit and subtact in case of loss)

and acoording to the question SP = 1200rs

So 0.8x = 1200

x = 1200/0.8 = 1500rs

So C.P is 1500rs.

If it's given that C.P is 1000rs and profit made is 20% 

Then it will be much more simple.

C.P is 1000rs so profit 20% will be 200rs.

So Profit = sp-cp therefore SP = CP + profit = 1000+200=1200rs.

Or If S.P is Given and Also Discount % is given you have to calculate MP

Example S.P = 200rs

Discount % = 80%

Find MP.

Simple Let M.P be X

So S.P after 80% discount will be 0.2x 

and according to question S.P = 200

So 0.2x= 200 

x = 1000rs = MP

Case 4: Combination Where MP CP SP are Mixed Together.

An article was purchased for Rs. 78,350. Its price was marked up by 30%. It was sold at a discount of 20% on the marked up price. What was the profit percent on the cost price?

Cost price = Rs. 78350

Marked price = 1.3*78350  = 101855( I told in the Start CP is Absolute 100% so If anything is Marked or Sold Above CP by ---% You just have to add that % to 100% and Convert it into it's relative decimal value)

Selling price = 101855*0.8= 81484[ Discount is calculated on MP so here MP is Absolute 100%, 20% discount that Means The product is being Sold at 80% of MP or 0.8MP)

Profit = S.P - CP = 81484 - 78350 = 3134

Profit% = (Profit/CP)*100 = (3134/78350)*100 = 4%

Case 5

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

1st- Basic method.

Find the C.P of 1 orange that will be 10/11

Find SP of 1 orange that will be 11/10

As it's clear SP>CP hence Profit will be SP-CP = 11/10 - 10/11 = (121 - 100)/110 = 21/110

Profit % = [(profit)/CP]*100 = [(21/110)/(10/11)*100] = [(21*11)/(110*10)*100 = 21%

2nd- LCM method.

Take The LCM The two numbers present in the Question i.e LCM of 10 and 11 = 110.

Now this Is the Amount Of oranges you will buy and sell and calculate the profit % on that.

So CP of 110 Oranges = 100rs

S.P of 110 Oranges = 121rs

Profit = 21Rs

Profit % = 21%[ calculates on the CP of 110 Oranges]

3rd - fastest Method but Confusing

Write The Purchase line First --- 11 oranges for 10

 -------------------------------------------------cross multiply-----                         

Selling Line 2nd                            10 oranges for 11 

11*11 will be SP and 10*10 will Be CP

Profit % = (11*11 - 10*10)/(10*10)*100 = 21%

Lets See one More Example

A man buys 8 pens for rs 9 and sells 9 pens for rs 8, Find profit or loss%?

By LCM methdo 

take lcm of 8 and 9 that will be 72

CP of 72 pens will be 81rs

SP of 72 Pens will be 64Rs

Clearly there is loss which will be equal to 81 - 64 = 17rs

Loss % = (17/81)*100 = 20.98 or 21%

BY Fastest Method.

Write the purchase line 8 pen for 9rs

---------------------------------cross multiply

write sale line                  9 pen for 8rs

C.P will be 8*8 = 64

S.P will be 9*9 = 81

Loss% will be (17/81)*100 = 20.98%

Case 6:- Dishonest dealer using false Weight and selling at Cost price.

A Dishonest dealer Professes to Sell the product at cost price but Instead of Selling 1000gm He sells only 900gm for 1Kg Wt

You don't need any Formula to Solve This Type of Question. You just have to use your own Mind here.

Now Look what the dealer is actually Doing here.

Dealer says He sell at Cost price Means He say He Sells at the price he purchases.

Now What amount He says He Sells = 1000gm

What Actually He Sells = 900gm

Now you can See here he is only selling 900gm and he is getting the oney for 1000gm

So this money from 100 Grams is His Profit OK.

Now how we calculate profit % ? We take CP as Base and Divide the Profit by CP.

Now look in this Question he is Selling 900 Gram and getting 100gram As profit.

So profit % will be (100/900)*100 = 11.11% 

One More Question 

A dishonest dealer Professes to sell the goods at cost price but instead of selling 1000 gms he sells only 800 gms for 1KG WT. Find his Gain% ?

Now Just Remember what He says He is Selling or what he gets paid for, he says he sell 1000gram

But What Actually He sells ? yeah exactly 800grams.

So how much he gets Extra or how much he cheats = 200grams

So profit will be (200/800)*100 = 25%

Case 7: Dishonest Dealer and also Selling Above Cost price.

A dishonest dealer Sells his Good 20% above the cost Price and Also cheats the Customer By giving them only 800gm for 1kg wt. What's his Profit % in the whole transaction.

We have to do the same stuff here Just Imagine. If he sells 1kg then how much will get paid for but also remember that he sells his good above 20% of CP Which means that if he sells 1000gm he gets paid for 1200gm. [ 20% above CP ka matlab yahi hua na ?]

So he gets paid for 1200gms and What he actually Sells here is ? Yes 800gms Only

So Profit will be SP - CP = 1200 - 800 = 400gm

Profit % will be (Profit)/CP*100 = [400/800]*100 = 50%

Case 8: When two Articles are Sold at Same Price but one at profit and one at loss and % profit = % loss.
In Such Cases there will always be a loss (%)which will be equal to [(Common Gain or Loss)]/10]^2 

Example - A man Sell two Wrist Watches One at a profit of 20% and one at loss of 20%. The selling price of each watch is 200rs. 

i) Find the Percentage of profit or loss.

ii) Net Amount of profit or loss.

i) As i told there will always be a loss in this case And % loss = [(common gain or loss)/100]^100

Now just put the value % loss = [(20/10)]^2 = 4%

Hence Loss % = 4%

ii) Net Amount of Loss 

So His Total SP was 200 + 200 = 400rs

He Suffers a loss = 4% Which means he sells his watch at 96% of their value i.e CP

So acording to Question 96% of CP = 400rs 

or 0.96CP = 400rs

CP = 400/0.96 

CP = 416.6667

So Net Amount of Loss = CP - SP = 416.667 - 400 = 16.667Rs

Case 9 - Goods passing through Successive hands.

It's a Lot like the method i told you yesterday about consecutive increase or decrease.

But Let's just Check it again.

A sells a good a profit of 20% to B and B Sells That Good to C at a profit of 25% If C pays 225 For It. What was it's Cpst Price for A.

So Just Asumme that CP for A was x

So he sells it at 20% profit That means he sells it at 1.2x

Now S.P of A = C.P of B

So Now B sells it to C at 25% profit

That means B sells it at 1.2*1.25*x 

Now C pays 225rs 

That mean 1.2*1.25*x = 225

so x = 150Rs

Answer CP for A = 150Rs.

Or you can Also use the formula which i told yesterday [x + y + (xy)/100]

Same way you can solve for 3 persons also.

Case 10 - CP of X articles = SP of Y Articles.

Very Simple If you know the trick behind it.

Eg - CP of 25 Articles is Equal to the SP of 20 Articles. Find the Profit or loss %.

Just write it This was 25CP = 20SP

Now Cross multiply So that Variables gets on One side of the equation and Constant gets on the Other Side.

So SP/CP = 25/20 

Now you just have to take that Elements on the opposite sides of Equation represents their corresponding value.

So in Equation SP/CP = 25/20. In front of SP the value is 25( So our SP will be 25)

And in front of CP the value is 20( So out CP is 20)

Now You know CP and SP calculating profit or loss is a child's play now but still we have to play it[ Personal Advice Always Believe in complete solution of the question, never leave the question in Mid Way ]

So as SP>CP there is profit

And profit will be [(SP-CP)/CP]*100 = (5/20)*100 = 25%

Another Example 

CP of 10 articles is equal to the SP of 12 Articles Find the profit or Loss %?

Do the same stuff again

10CP=12SP

Cross multiply now.

SP/CP = 10/12

So SP = 10

and CP = 12

So clearly there is a loss And loss % = (Loss/CP)*100 = (2/12)*100 = 16.66%

Case 1: Marking Above x% and giving discount of y%, Total profit or loss.

Eg A person Marks his good above 50% of CP and Gives Discount of 20% Find his Profit %.

The easiest way to solve this type of question is to assume the CP as 100

So CP is 100

M.P will be 50% above CP that will be 150

Now he gives discount of 20%

As discount is caculated on MP so SP after deducting the discount will be 150*0.8 = 120

Now SP = 120, CP = 100 So profit % will be 20%.

Case 12 - Decrease in Price of Commodity allows A person to Buy X quantity more of an item.

EG - When the price of sugar decreases by 10%, a man could buy 1 kg more for Rs 270. Then, the

original price and final price of the sugar are ?

Now remember i told you a formula yesterday Which Goes something like this[ (How Much It is decreased)/( What It Becomes after decrease)*100].

So this Question is Implementation of that Formula only.

Price is decreased by 10%.

So Man can purchase how much extra now ? Apply the formula ( How much decrease/ What It becomes )*100 = (10/90)*100 = 100/9 %

So man can buy 100/9 % more sugar now.

Lets Assume that originally He used to buy x kg of sugar

And as it's given in the question He can Buy 1 KG more. So that means that 100/9 % of x = 1kg

(100/900)*x = 1 

x = 9kg.

Now Original Quantity = 9kg

So Original Cost = 270/9 = 30Rs/KG

Increased Quantity = 9+1 = 10kg

So Final Price = 270/10 = 27RS/kg

Case 13

A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the CP should be marked on the items?

Simple way to solve this Question is By Assuming MP as X and CP as Y.

So Let MP be X, So SP  after 25% discount  = 0.75x

And He also Wants to Again 50% on CP, So SP in Terms of y will be = 1.5y

Now Both SP are Equal So 

0.75x = 1.5y[ Now we have to find MP with respect to CP So express the equation in terms of Y]

x = 2y

or x = 200% of Y

So he Should marks his Goods 100% above the CP. 

Case 14:- Successive Discount.

We all used to get Amazed when we heard deals like 50% + 49% discount, I always used to wonder how can they sell their product at 1% price LOL. Then i studied % in class 7th and it became clear to me that's it's another way of looting commom man.

So what actually is Successive Discount. 

Successive simply means anything which is applied in succession ( ek ke baad ek apply karna )

So When Pantaloons Say 50% + 30% off It doesn't mean you will get the discount of 80%. If they wanted to give you 80% discount( which they would never do) then they would simply have written 80% instead of 50% + 30%.

For Example You wen to Pantaloons or levis whatever And You Like a jeans Whose MP is 1000rs, and there is a discount of 50% + 30%. So Now You have to apply the 50% discount, By applying that New MP will become 500rs and Now On this 500Rs you will apply the next 30% discount to get the final SP which will be 350Rs.

So Lets See some Examples.

There are 2 Successive discount on Watch Whose MP is 2000rs. the first Discount is of 40% and other is of 20%.

The Good thing with successive discount is that you can apply The discount in any way you want, that means you can apply 20% discount first and if you want you can apply 40% discount first. The answer will remain the same.

So now Lets Apply 40% discount on 2000rs. After applying 40% discount the MP will become 1200rs and On that 1200 we apply another 20% discount So the final SP will become 960Rs.

Now Do the Other Way. First Apply 20% discount on 2000rs So new MP will be 1600 Rs Now apply 40% discount again. And the Final SP will be 960 Rs

You can see the answer is same in both the cases.

But I will tell you simple method Just Multiply It. 

I means MP is 2000 You want to apply 40% and 20% Discount Just do it like this was 2000*0.6*0.8 = 960

Sometimes It's Also Asked two successive discount of 30% and 40% is Equal to what Single Discount.

No need to worry Just do the regular Stuff. If MP was 1 after 30% discount it will become 0.7 and after 40% it will be 0.6

So multiply the values.

0.7*0.6 = 0.42. 

Now This 0.42 is The Final SP 

So total Discount will be equal to 1- 0.42 = 0.58 or 58%

Lets see 1 more example.

What will the Single Equivalent discount for two Successive Discount of 40% and 50%?

Let MP = 1

Now apply discount 0.6*0.5 = 0.3 = SP

So Discount = 1- 0.3 = 0.7 or 70%.

Case-15: Equation Based Question,
 it's not a single case many Question can be Made From This case But basic idea is you have to make a mathematical Equation To Solve Such type of Questions.

A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual CP of the article.

Let Assume the CP of the article was x. So according to Question The SP must have been 1.25x

Now He buys the article at 10% lesser price that means he buys it at 0.9x 

And he sells it 2rs less which means at 1.25x - 2

He will still get 25% profit But This 25% will be calculated on 0.9x because it's the new CP

So 1.25x - 2 - 0.9x = 25% of 0.9x

0.35x -2 = 0.225x 

0.35x - 0.225x = 2

0.125x = 2

x = 2/0.125 = 2000/125 = 16

So CP = 16.

Another One

A trader Sells an Article at 25% profit If he had Sold the item at 10 Rs. more the profit would have been 30%. Find The CP?

It's very simple question In this type of question just assume CP as x.

And Convert the % value of Profit into decimal and Then Solve the question Accordingly.

25% of x = 0.25x

and 30% of x= 0.3x

Now in the Question it is said The dealer would get 10rs more if the profit is 30% Or the difference between 25% profit and 30% profit is 10Rs

So 0.3x - 0.25x = 10

0.05x = 10

x = 10/0.05 = 1000/5 = 200

One More Question, A dealer Sells an Article at 20% profit If he had sold the article at 500rs less he would have suffered a loss of 30%. Find CP

Just Take CP as x

so 20% profit will be = 0.2x

30% loss = -0.3x[ remember loss is assigned as negative]

So according to Question the Difference between 20% profit and 30% loss is 500rs

So 0.2x - ( -0.3x) = 500

0.2x + 0.3x = 500

0.5x = 500

x = 500/0.5 = 5000/5 = 1000



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