### Discussion :: Profit and Loss - General Questions (Q.No.4)

4. | In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? |
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Answer: Option B Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 125% of Rs. 100 = Rs. 125 New S.P. = Rs. 420. Profit = Rs. (420 - 125) = Rs. 295.
Video Explanation: https://youtu.be/bQA8SB8ycbw |

Vinoth said: (Jun 29, 2010) | |

Profit% = (Gain*100)/CP right. But in the above problem SP has been substituted instead of CP? |

Sundar said: (Jul 7, 2010) | |

Hi Vinoth, Please read the question very carefully. What percentage of the selling price is the profit?That's why here SP is substituted. Have a nice day! |

Vaishali said: (Jul 8, 2010) | |

Same problem that profit=gain*100/cp, but how can we change formula. I think first we have to calculate the profit% then should find what % of P it is na? |

Anshuma Chugh said: (Jul 14, 2010) | |

Maths is so complicated, Is not so, needs so much practice. |

Selvam said: (Sep 28, 2010) | |

Hai friend I can't unterstand your concept please explain one more time. |

Kavi said: (Dec 23, 2010) | |

Somebody please explain me the question clearly. |

Nitesh said: (Jan 5, 2011) | |

Let CP=1000 profit=320% But profit = SP-CP; 320 = SP-1000 SP=1320; Now given that CP is increased by 25 % then CP becomes 1250 and SP is constant hence Profit = SP- CP profit = 1320-1250=70 therefore answer is 70 |

Vivek said: (Jan 5, 2011) | |

You can assume 100 or x becoz for simplicity. |

Mahboob Alam said: (Jan 8, 2011) | |

How can we assume the value of C.P. is 100. If the value of C.P. is not given ? Can we take the value of CP is x? |

Deepak said: (Jan 21, 2011) | |

I cant understand method of this question please explain in simple format. |

Malini said: (Jan 26, 2011) | |

Let me explain you clearly: In most of the problems assume cp as 100 then only it will be easy. now let us assume cp=100 profit is given 320% we know p=sp-cp then sp=p+cp so sp=420 Then it is given cp is incresed by 25% so cp=alredy assumed as 100+now increased by 25% cp=125 sp is always constant(given in question) so now sp=420 cp=125 p=sp-cp =420-125 =295 p%=p/cp*100 But here it is specifically asked for sp(read the question) so p%=p/sp*100 =295/420*100 =70% |

Archana said: (Feb 13, 2011) | |

I had not understood the explanination. Can you please explain me it again. How can we assume cp to be 100? |

Habib said: (Feb 23, 2011) | |

Maths & Physics are completely based on assumption based foundations....even in this example no data about CP is given...so we have no choice just assume a simplified value (eg 100 or 1) and base your calculations upon that !!!! |

Dinesh said: (Mar 28, 2011) | |

Good explanation malini. |

Khaleel said: (Mar 29, 2011) | |

Hi nitesh if we take cp=100 your principle not works. |

Sinu said: (Apr 27, 2011) | |

Thanks malini. |

Swimmi said: (Jun 26, 2011) | |

Why sp 420 is calculated when it is given that sp will remain constant? |

Kanakam Vinay said: (Aug 2, 2011) | |

Nitesh your Answer is verry nice and Simple. But 1000 is Working 1000 increased by 25% it became 1250 , but if u take 100 incresed by 25% it became as 125 then the Problem is Wrong .. If we assume anything it will be satisfied to all the Methods. |

Hari Haran said: (Aug 19, 2011) | |

What percentage of the selling price is the profit? In maths formula is a basic, but we have to understand it in different views. Then we make it up easy. Sundar is correct. |

Balavignesh said: (Aug 31, 2011) | |

Profit=selling price-cost price But profit is given in percentage and i thought that as profit percentage. But we use it like profit i.e. Rs.320. How is this possible? |

Eshan said: (Sep 9, 2011) | |

In last formula %profit=(CP*100)/profit according to it ans is A.30% |

Rohini said: (Oct 2, 2011) | |

We don't have any formula p% = p/sp*100 We have sp = (100+p%)*cp/100 |

Saran said: (Nov 2, 2011) | |

How is selling price is 420. ? |

Danish.Jamia said: (Nov 13, 2011) | |

You have taken wrong formula, the correct form is (profit*100) /cp. |

Kishan Chand said: (Dec 2, 2011) | |

The correct answer is 240%. Thats because, If you are buying of Rs. 125. And solding it of Rs 425. Now you calculate the percentage of profit. |

Asit said: (Dec 25, 2011) | |

@kishan chand your thought is absolutely correct, but the question is about percentage of only selling price, you are calculate it from the cost price. Now you understand or not? |

Radha said: (Jan 17, 2012) | |

Very niceexplanation malini. |

Mittalvarun2011 said: (Apr 28, 2012) | |

Thanks Nitesh and malini for such a nice explanation. |

Merlin said: (Jun 9, 2012) | |

Why we are taking cp as 100? In what cases we should assume in that way. 2. Why cannt we take that as x as in above sums. |

Sagar Khurd said: (Jun 10, 2012) | |

25% cp is 1250 how that value get. |

Mohana said: (Jul 12, 2012) | |

How they have taken the C.P value = 100 even it gives change to assume any number like 1,2,3, etc., |

Dinu said: (Jul 14, 2012) | |

@Mohana. They have given profit%=320%. So to calculate profit we use the formula profit%= (profit*100) /C.P. If you assume C.P=100 then always the profit% = profit for this simplicity we always assume C.P=100. |

Ann said: (Sep 8, 2012) | |

Good explanation Malini! |

Lekan said: (Oct 7, 2012) | |

Alright I have another method here without assumption. First things first. P=SP-CP. Since P=(320/100)CP Then (320/100)CP=SP-CP. SP=(420/100)CP Next thing is getting the second equation. Our target is "what percentage of the selling price SP is the profit,P if we have a new cost price of (125/100)CP while SP remains the same?" So keep another P in mind which is x per cent of SP. Therefore equation2 is xSP/100=SP-(125/100)CP So xSP=100SP-125CP. SP=(420/100)CP xSP=100SP-125CP Eq2. Substituting for SP in Eq2 then we have x(420/100)CP=100(420/100)CP-125CP xCP420/100=420CP-125CP. xCP420/100=295CP. x=295/4.2 x=70.23. Note it has to be an approximated value according to the question which is 70. |

Sujith Shetty said: (Dec 3, 2012) | |

Just assume cost of price is 100 then profit is 320 so total cost of product is 320+100=420 if cost increases 25% i.e 125 then profit decreases 420-125=295(profit) 295/420*100=70% |

Nids said: (Mar 21, 2013) | |

Lets assume cost to be 10. profit = 320/100*10 =32. S.P = CP + P =10+32 =42. Now cost increased by 25% (25/100*10=2.5) =10 + 2.5 =12.5. SP remaining the same 42 SP=C + p 42 =12.5 + x 29.5 = x. So, If 42 is 100, how much would be 29.5? Cross multiply 42=100. 29.5=? Ans: 70. |

Sandy said: (Aug 6, 2013) | |

Why don't we do like this: We know that p = S.P-C.P. If x% be selling percentage of profit then, x*S.P = S.P-C.P. S.P- (x*S.P) = C.P. S.P (1-x) = C.P. (S.P/C.P) = (1/1-x). Now when we see the problem he given a clue that p = 320% (C.P). S.P-C.P = (320/100) (C.P). S.P-C.P = (3.2) C.P. S.P = (3.2) C.P+C.P. S.P = (4.2) C.P. S.P/C.P = 4.2 =>A. When C.P increases 25%, S.P is remains same then. S.P/ (C.P+ (25%C.P) ) = (1/1-x). S.P/ (1+0.25) C.P = (1/1-x). S.P/ (1.25) C.P = (1/1-x). (1/1.25) (S.P/C.P) = (1/1-x). Substituting from A (S.P/C.P) = 4.2. (1\1.25) (4.2) = (1/1-x). (3.36) = (1/1-x). (1-x) = (1/3.36). 1-x = (25/84). x = 1- (25/84). x = (59/84) = ~70% (approximately). |

Pretty said: (Aug 20, 2013) | |

So the conclusion is that we can assume any value for cp if not mentioned? |

Angelin Alfred said: (Sep 16, 2013) | |

Here, profit % is calculated on SP i.e. 420. But, it should be calculated on CP i.e. 100. |

Priti said: (Sep 30, 2013) | |

There is some confusion for profit% formula. Please give me answer ? |

Ram said: (Oct 10, 2013) | |

If question asking to Profit % on SP then Formula should be used - Gain % = profit*100/SP. If question asking to Profit % on CP then Formula should be used - Gain % = profit*100/CP. |

Jitesh Kumar said: (Oct 20, 2013) | |

@Nitesh. Your answer is wrong. 25% of 1000 is 1250(right). & 320% of 1000 is 1320(how?). 32% of 1000 is 1320. 320% of 1000 is 3200. So, Let C.P = 1000. profit = 320%. But profit = S.P - C.P; than S.P = 1000+3200. = 4200. Now given that C.P is increased by 25 %. Then C.P becomes 1250 and S.P is constant. Hence, = (4200-1250)/4200*100. = 70.23. But if you make C.P is 100 than it will be easy. |

Payal Sharma said: (Oct 21, 2013) | |

I understood everything but. Why you have taken S.P instead of C.P in the formula of profit percentage. And if its a theorem or formula so exactly where-2 we need to use this method. |

Anurag said: (Oct 22, 2013) | |

@Payal. Question itself is asking 'What percentage of selling price is the profit'. |

Anurag said: (Oct 22, 2013) | |

@payal its not the profit percentage formula. The required percentage asked is "what percentage of selling price is the profit". So, (profit/S. P) *100 is the required percentage. |

Vikash Kumar said: (Dec 23, 2013) | |

But here it is specifically asked for sp (read the question). |

Chandranaik.M said: (Jan 26, 2014) | |

Please sir give me Answer. How we get 420 in denominator? Actual formula for gain = (gain*100/CP). |

Jebestin said: (Jan 31, 2014) | |

Hi @Chandranaik. Read the question it is given, what percentage of the selling price is the profit? So they are calculating like: x% of 295 =420; x=(295/420)*100; |

Varun said: (Mar 1, 2014) | |

thax guys for explain clearly |

Nza said: (Mar 8, 2014) | |

Yes what you did is good. Please this also challenges me. You can help me. Assume that the district tax revenues grow at 25%. The district authority believes that its financial needs will be satisfied when the tax revenues double. As the local revenue collection officer, you are approached to tell when that will happen, holding other factors constant. |

Hasan said: (Jul 2, 2014) | |

Very nice @Malini! I got you in the question it is mentioned clearly that what percentage of the selling price is the profit? But from childhood we have been studying that profit could only on C.P. |

Rukhsaar said: (Jul 8, 2014) | |

Formulae is P% = P/C.P*100 then why we are taking 420 which is S.P? |

Roohi said: (Jul 18, 2014) | |

How you have calculated 25% for cost price? If CP is assumed as 100. |

Bhavi said: (Aug 26, 2014) | |

The answer is 236% is we substitute CP=125. |

Kalyani said: (Sep 18, 2014) | |

How we will get the value 420? |

Santosh said: (Sep 19, 2014) | |

Let me explain, 1) Profit is 320% of Cost ==> Profit = (320/100)*CP. Consider C.P is 100 then Profit = (320/100)*100 = 320. Now Profit = SP-CP. therefore, 320 = SP-100. So, SP=420. 2) If the Cost increase by 25% ==> CP=100+25 = 125. 3)But the selling price remains constant ==> SP=420 (from 1st part). Profit = SP-CP = 420-125 = 295. 4) What percentage of the selling price is the profit? <<< for example, X% of Y is equal to (X/100)*Y >>>> <<< 2% of 5 ==> (2/100)*5 >>> From the above example, what percentage of the selling price is the profit==> What percentage = ? Of Selling Price = SP. Is Profit = Profit. (?/100)*SP = Profit. Therefore, ? or Required percentage = (Profit * 100)/SP. Required percentage = (295*100)/420 = 70%(approximately). |

Imran Ali said: (Oct 25, 2014) | |

If we take cost prize 1000, then profit will not be 320, cause in question profit is 320 percent of 1000, which is not equal to 320. |

Ravi said: (Dec 26, 2014) | |

We are all know that gain% in terms of C.P price but in the given problem gain% in terms of S.P. |

Vanitha said: (Jan 23, 2015) | |

I have one doubt if the question is asked like what's the percentage of the selling price is the profit means we have to use denominator as s.p ah? |

Rinki said: (Feb 2, 2015) | |

I have a doubt here in question's 2nd part here we know that %profit calculated by CP but here? |

Vijayalakshmi said: (Feb 9, 2015) | |

Please give shortcut for this. |

N Raju said: (Feb 21, 2015) | |

@Nitesh. If I take CP = 100 I'm getting wrong answer can please help me? |

Nitish Rajbhar said: (Apr 3, 2015) | |

Let, Cp = x & Sp = y. According to question, The profit is 320% of the cost, Gain = (320/100)*x = 3.2x. Gain = Sp-Cp. 3.2x = y-x. x = y/4.2....(1). If the cost increases by 25% but the selling price remains constant. Cp = (x+x*25%). = (x+ 0.25x). = 1.25x. Sp = y (because of constant). Then, Gain = y-1.25x. By equation (1) put the value of x in above equation. Gain = y-1.25*(y/4.2). Gain = y*(.70). = 70% of y. Thank you. |

Usman said: (Apr 21, 2015) | |

New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420. Profit = Rs. (420-125) = Rs. 295. Required percentage = 295x 100% = 1475% = 70% (approximately). This step 1 didn't get. |

Anjana said: (Jul 16, 2015) | |

We know that. P=S.P-C.P....(1). Here the profit is 320% of the cost, so. P= (320/100)*C.P....(2). Substitute (2) in (1) instead of P. We get (320/100)*C.P = S.P-C.P....(3). From the equation (3) we can calculate the s. P in terms of C.P as. S.P = (420/100)*C.P....(4). Next we take the second condition: the cost is increased by 25%. The new C.P is C.P+(25/100)*C.P....(5). The equation (5) is substituted in the equation (1) instead of C.P. We get P =S.P - (C.P+(25/100)*C.P). P = S.P-C.P(1+(25/100))....(6). We are calculating new profit (P) is how the percentage of the selling price (S.P). Hence in equation (6) substitute C.P in terms of S.P. We know the relation between s. P and c. P in equation (4) from that. C.P = (100/420)*S.P....(7). Substitute this c. P in to equation (6). P=S.P-(100/420)*S.P*(1+(25/100)). By solving we get : P = S.P (1-(125/420)) = 70% (approximately). |

Jay said: (Aug 8, 2015) | |

Can anyone explain me once again I have to look at it? Can anyone explain me about ratio proportion? |

Sathish said: (Aug 12, 2015) | |

60.90% should be the right answer for this question. SP should remain constant was mentioned at the question, so answer must be 60.90%. Thanks. |

Sathish said: (Aug 12, 2015) | |

Simple, Assume Cost = 100 Profit gained is 320%. So SP = 320+100 = 420. Now CP increase by 25, New CP = 125. Gain now = 420-125 = 295. Gain % with respect to SP (as per question) = 295/420 x 100 = 70%. |

Jaspreet Singh said: (Aug 17, 2015) | |

Thank you so much to every one for nice explanation. Great site to learn. |

Sowmya said: (Sep 18, 2015) | |

Thanks you so much every one for nice discussion. |

Mahnoor said: (Sep 21, 2015) | |

I can't understand this question please. Explain me simple method + shortcut? |

Rahul Singh said: (Sep 30, 2015) | |

Let C.P = 100. When C.P = 100 then profit will be profit = (320/100)*100 = 320. When C.P = 100 and Profit = 320 then S.P = (C.P+Profit) = (320+100) = 420. If the C.P increases by 25% Then C.P = 125 and S.P according numerical remain constant. So S.P = 420. Now profit will be profit = (S.P-C.P) = 420-125 = 295. So Required % = (295/420)*100 = approx (70). |

Abhishek said: (Oct 15, 2015) | |

236% is the answer because final profit is to be calculated on CP not on SP hence 295/125 = 236%. |

Nitu said: (Oct 30, 2015) | |

I can't understand the solution. |

Adeesh Dhiman said: (Nov 22, 2015) | |

Why did put in the question p = gain/sp*100? |

Siva Krishna said: (Nov 27, 2015) | |

Guys give some more examples on profit and loss so that we can practice and understand too fast instead of this much confusion. |

Mahi said: (Dec 4, 2015) | |

We have calculated Profit and SP in first case but why to take 125% for new CP, Although CP is 25%? |

Priya.D said: (Jan 30, 2016) | |

How did you assume C.P value? |

Sanket Wankhede said: (Mar 1, 2016) | |

How did 420 came into existence? |

Vijay said: (Mar 3, 2016) | |

Hello @Vindo, He finding percentage, not profit percent. |

Supriya said: (Mar 31, 2016) | |

How to calculate 1475/21? How did 70% come? Please explain? |

Vinay said: (Apr 2, 2016) | |

Good question @Supriya. |

Sakharam said: (Apr 8, 2016) | |

In solution see Initially CP is 100 and SP is 420, so Profit is 320%. Now CP is 125 and SP is 420, so Profit should be 420 - 125 = 295 means 236% should be the correct answer. |

Deepika said: (Jun 9, 2016) | |

Thanks for your clear explanation @Malini. |

Django Boy said: (Jun 9, 2016) | |

The point is in 'what context' the profit percentage is to be calculated? Is it relative to cost price or selling price? Well!, when you're asked to find the profit %, its relative to the 'selling price'. That's why in the above problem the answer is 70%. If we consider the cost price as the base to find the profit %, then it would be 236%. But this is wrong. To understand this more, Draw a pie diagram, taking the selling price (420) as the full circle and mark the proper fractions for cost price (125) and for the profit (295). Just see the portion of profit and determine the area covered in the circle, that's the profit %. |

Hariom Dubey said: (Jul 7, 2016) | |

In general, we calculate profit % relative to C. P (because CP remains constant) but if we are asked to calculate profit % relative to S. P (as in this question) we have to take S. P. As base price provided S. P is given constant. Since in this question S. P is given constant, we can take S. P as the base price. |

Bhushan said: (Jul 30, 2016) | |

From where the value 1475 come? Give explanation. |

Srinivas said: (Aug 5, 2016) | |

We calculate the profit percentage with the help of cost price but in above problem why we are using selling price, tell me the reason. |

Chirag said: (Aug 24, 2016) | |

Hey, @Nitesh, you find here to profit not profit %, then how can you say that the answer becomes 70. Read question carefully and then go ahead. |

Houdini said: (Oct 22, 2016) | |

How can you change the sp there is clearly written that sp remains constant? |

Ramesh said: (Dec 27, 2016) | |

CP = 125 SP = 420 Profit = 320. For SP is 420 we got 295 profit. Convert it into 100(%). (295/420) * 100 = 70%. |

Yb Patil said: (Dec 31, 2016) | |

We always assume cp =100 because loss and gain is always reckoned on cost price. That's why we assume (if not given ) cp = 100. |

Amrita said: (Jan 31, 2017) | |

Let CP =100 rs. From ques. SP = 320% of CP = 100+320 =420 rs. Now ques says that CP is increased by 25% .it means now CP = 125 rs But, SP remains constant. Now Profit = 420 - 125=295 rs From the question, we have to find out the PROFIT % at SP(420 rs.) So P% = (295/420)*100 = 70%. (SP-CP)/CP is not a formula actually. this is only for our comfort to find out an easier way to solve problems. |

Girija said: (Feb 10, 2017) | |

A Horse is sold at a profit of 25%. If both the CP and SP are Rs. 200 less, the profit will be 5% more. The cost price is? Can you please help me to solve this? |

Sandeep Singh Sandhu said: (Feb 19, 2017) | |

@Girija. SP = 1.25CP FOR 25%PROFIT. (SP -200) = 1.3(CP-200) FOR 25% MORE PROFIT. SP-200 = 1.3CP-260. 60 - 1.3CP - 1.25CP. 60 = 0.05CP. CP = 60/0.05. CP = 6000/5. CP = 1200. |

Suresh said: (Jun 25, 2017) | |

Yes, the cost price must be 100, let me clarify. Profit % =320 ,how the profit is 320 because, Profit % =profit *100/ CP ----(1). , if CP is 100, equation (1) becomes, 320=profit *100/100 and then 320 = profit so the given answers is correct. |

Vaibhav Pund said: (Jul 29, 2017) | |

It's so simple. Assume CP=100. Then SP=320% of CP=(100*320)/100=320+100=420. CP increased by 25%=100*25%=(100*25)/100=25+100=125, Profit=SP-CP=420-125=295. Profit %=( gain/CP)*100. But we have to find profit% with SP. So, Profit %=(295/420)*100=70%. |

Deepak said: (Aug 21, 2017) | |

Hello, The % profit =(profit/cp)*100. But here the % profit =(profit/sp)*100. |

Charulatha said: (Aug 30, 2017) | |

The profit%=(sp-cp)/cp*100. Then how we take as profit%=(sp-cp)/sp*100. |

Sushanta said: (Sep 29, 2017) | |

I think profit is 320% of the cost then why you guys taking profit is 320 rupees. Then what rupees is cost? |

Harika said: (Oct 3, 2017) | |

Here given in that question is profit is 320% of the cost, right? Then why you guys taking is as 320 rupees. Can you please anyone can tell me the answer to my question? |

Akash said: (Nov 22, 2017) | |

@Harika. Let's say cost price = 100. Profit =320% of cost price (given) So %profit= (profit/cost price)*100. 320=(x/100)*100. X = 320. |

Alka Raikwal said: (Dec 30, 2017) | |

Very good explanation, Thanks @Malini. |

Gaurav said: (Jun 14, 2018) | |

P=SP - Cp. 3200 = x - 1000, x = 2200. Now, 3200=x-1250, X=1950, 1950/1250*100= 70% approx. |

Ankit Yadav said: (Jul 13, 2018) | |

How they can use 420 it is SP? Explain me in detail. |

Vaishnavi Shikha said: (Jul 31, 2018) | |

Sp= cp + profit. So, 100+320=420. |

Varun said: (Sep 14, 2018) | |

Can anybody explain why we take 420 in denominator we always take CP in the denominator? |

Anjali K said: (Jan 26, 2019) | |

@ALL. According to me, the solution is; p = (320/100)*cp----> from 1st sentence. p = 3.2cp. sp = 3.2cp+cp(form p=sp-cp). sp = 4.2cp. New cp: cp = cp+(25% of cp). cp = cp+2.5cp = 3.5cp. p = sp-cp=.4.2cp-3.5cp ===>0.7cp = 70%. |

Harika said: (Feb 21, 2019) | |

Good explanation, Thank you. @Malini. |

Bala said: (Mar 13, 2019) | |

I didn't understand. How can you fix C.P value 100? Please tell me. |

Mongam said: (Mar 28, 2019) | |

I am not understanding. Please, anyone, help me. |

Dnayak said: (Jun 27, 2019) | |

Yes, it is 236. |

Disha said: (Jul 4, 2019) | |

How come 1475/21 = 70%? |

Vaishnavi said: (Jul 16, 2019) | |

Assume: C. P=x. S. P=2x. Profit=3x. Now, Profit = ( sp-cp). = 2x-x = x. Now. Profit% = cp/profit * 200. =x\x * 100= 100. |

Avinash Reddy said: (Jul 30, 2019) | |

Thanks for giving the solution @Anjali K. |

Sourav said: (Aug 7, 2019) | |

%p = {(sp-cp)/cp} * 100. |

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