- What is Discount?
- What is successive discount?
- Case: Successive vs One Time Discount?
- What is marked price?
- Case: Finding Marked Price from Profit %
- Case: Finding marked price from Selling price
- Case: Finding % Profit / loss in MP-Discount
- MOCK TEST
- Answers with explanations and shortcuts
What is Discount?
In the garment stores, you’ve come across this sign many times: “HURRY! 20% OFF!!”
That 20% is called discount.
Suppose a Music CD has price tag of Rs.100 and the shopkeeper is offering 20% discount.
That means 20% less on the price tag.
The price you’ve to pay
=Rs.100 minus 20% of 100
=100-(20×100/100)
=100-20
=Rs. 80 you’ve to pay, to buy that music CD.
But in exam, we don’t have no time to do such lengthy calculations.
So just think in your head:
20 percent discount means you’ve to pay 100 percent minus 20 percent=80 percent of the price tag.
% means one upon hundred (1/100)
So 80% means (80/100=0.8)
So you’ve to pay 0.8 times the original price.
=0.8 x 100
=Rs. 80
What is successive discount?
It means discount on the discount. (just like Compound Interest rate= interest on interest)
The original price of a music CD is Rs.100. A shopkeeper offers 10% discount on this music CD and then again offers 20% discount on the new price. How much will you have to pay, finally?
Phase I: 10% discount
So new price = 0.9 x original price. (by the way, how did we get 0.9 ? well 10% discount means you’ve to pay 90%. And 90% means 0.9)
Phase II: 20% discount
=0.8 x new price
=0.8 x 0.9 x original price.
It means, after successive discount of 10% and 20%, the final price you’ve to pay
=0.72 x original price.
=0.72 x 100
=Rs.72
If it was successive discount of 20% and then 10%? Still answer will remain same. ORDER or sequence doesn’t matter.
Let’s test our skill with an actual question from SSC/FCI Exam taken in Nov 2012.
Q1. A dealer buys a table listed at Rs.1,500 and gets successive discounts of 20% and 10%. He spends Rs.20 on transportation and sells it at a profit of 20%. The selling price of the table is
- Rs.1,320
- Rs.1,350
- Rs.1,360
- Rs.1,380
Think in your head:
20% discount =0.8 x original price (this is our new price)
10% successive discount= 0.9 x New price=0.9 x 0.8 x original price
Finally dealer had to pay: 0.72 x original price.
Then he invested Rs.20 on transport, so his total investment (cost price) is
(0.72 x original price) + Rs.20
And ultimately he sold It @20% profit.
20% profit means 100%+20%=120%
=1.2 times the investment (cost price).
=1.2 times [(0.72 x original price) + Rs.20]
In the examhall,only write following line and do the math, don’t waste time writing everything or multiplying numbers @every stage.
=1.2 times [(0.72 x 1500) + Rs.20]
=1.2 [1080+20]
=1.2 [1100]
=Rs. 1320
(I hope you know quick multiplication with 11, basically 12×11= in 12 you do:1|(1+2)|2=132)
Case: Successive vs One Time Discount?
Q. Jethalal, has a mobile phone with price tag Rs.12,399/-. He is offering two schemes to you
- Buy it at one time discount of 30%
- Buy it at two successive discounts of 15% and 15%
Which of the above scheme is more beneficial to you (customer)?
Long cut (tiresome and boring calculation)
Scheme A | Sheme B |
Discount offered =30% of 12,399 =0.3 x 12,399 =3719.7 |
Phase I 15% of 12399 =1859.85 Rs. (discount I) So new price : 12399 MINUS 1859.85=10539.15 Phase II: (second discount) =15% of 10539.15 =0.15 x 10539.15 =1580.8725 (discount II) Total discount =1859.85 +1580.8725 =3440.7225 |
We are getting more discount in Scheme A compared to Scheme B.
So, from customer’s point of view, Scheme A is more beneficial.
^Very lengthy and tiresome calculation isn’t it?
Well, if you look at it carefully, the price tag Rs.12,399/- is irrelevant here.
Shortcut (almost none calculation)
Scheme A | Scheme B |
Discount offered=30% Final price you’ve to pay =0.7 times original price. |
Successive discount 15% (two times) Final price you’ve to pay =0.85 x 0.85 x original price =0.7225 x original price |
In Scheme A, you’ve to pay less price compared to Scheme B. Because 0.7 < 0.7225
So, from customer’s point of view, Scheme A is more beneficial.
Sidenote: you can do 85×85 with Vedic shortcut (square of numbers ending with five)
Square of 85
=8|5
=(8x(8+1)|25
=8*9|25
=7225
I hope discount and successive discount is clear. Moving to the next topic.
What is marked price?
Before that, answer this question:
Why do shopkeepers give discount?
Well it’s a marketing propaganda to seduce customers.
I’m running a jeans store. I bought a pair of jean for Rs.100 (cost price).
Now I put a new tag on it Rs.500 (marked price) and then put a huge poster outside my shop: “50% OFF on any item!”
From buyer’s point of view it looks very attractive “wow 50% discount!!”
But in reality, I’m making huge profit. Because 50% discount on Rs.500= You’ve to pay Rs.250, while I had invested only Rs.100! so my profit=(250-100)=Rs.150
Marked price=this new price tag Rs.500. Discount is given on marked price. If we want to visualize it, here is the diagram:
Mind it: Profit or loss is always calculated on actual investment (Cost price), unless they specifically instruct you do something else.
Time to test the skill with actual questions
Case: Finding Marked Price from Profit %
Q. Jethalal bought a Nokia mobile phone @ Rs. 800. He sold it to Master Bhide after allowing a discount of 10%. In this deal, Jethalal made a profit of 12.5%. What was the marked price?
- Rs. 1,000
- Rs. 1,100
- Rs. 1,200
- Rs. 1,300
Profit is always calculated on actual investment (cost price).
Cost Price: Rs.800
The question says, profit =12.5%. What is the profit in rupee terms?
Long cut | Shortcut |
=12.5% x 800 =(125/10)x (1/100) x 800 =Rs. 100 |
12.5% =1/8 (percentage to fraction conversion table). So, 12.5% x800 = (1/8) x 800= Rs. 100 |
Anyways in either method, profit is Rs.100…Fact (i)
Jethalal gave 10% discount on marked price. So customer Bhide Master had to pay only
90% of the Marked Price.
=0.9 times the marked price
=this is the money Jethalal received from customer.
Jethalal’s actual profit
=the money he received from customer MINUS his original investment.
=0.9 times Marked price MINUS Rs.800
But recall fact (i), Jethalal’s profit is Rs.100
Therefore
100=0.9 times Marked price – Rs.800
100+800=0.9 times marked price
900=0.9 x MP
MP=900 x 10/9
MP=Rs. 1000.
Final Answer: marked price is Rs.1000
In the exam hall, directly frame the equation: 0.125 x800 =(0.9 xMP)-800
Let’s try another one.
Case: Finding marked price from Selling price
Q. Master Bhide, bought two pens for Rs.37.40 at a discount of 15%. What must be the marked price of each of pen?
- Rs.11
- Rs.44
- Rs.33
- Rs.22
Discount of 15%, means Master Bhide (customer) paid (100-15)=85% of the marked price.
=0.85 times the marked price
But question also says he paid Rs.37.40, Therefore
37.40=0.85 x MP.
MP=3740/85
=(374x 10)/ (17×5)
=(374 x 2)/17
=(22×2)
=44. (Sidenote, if you don’t know the multiplication table of 17, then use approximation method explained in earlier article. CLICK ME)
Most important part: Rs.44 is the marked price of two pens. So marked price of each pen =44/2=Rs.22
Answer is (D)
In the actual exam, rough paper calculation: =37.4/(0.85 x 2)
Case: Finding % Profit / loss in MP-Discount
Jethalal marks the price tags of all his mobile phones, 10% above the cost price. And then He offers 10% discount on their marked prices. What is his profit or loss?
- 1% profit
- 1% loss
- 5% profit
- No profit No loss.
Assume his total investment is Rs.100 (=cost price). Well we can assume total investment as “CP” or “x” or “y” or anything but assuming Rs.100 saves the time of calculating percentages later on.
Marked price
=10% above cost price
So price tag (marked price) is
100%+10% of Cost price
=110% of cost price
=1.1 x cost price
=1.1 x 100
=Rs. 110
Now he offers 10% discount on marked price, so customer has to pay only
0.9 times the marked price
=0.9 x 110
=Rs.99
Verdict: His investment is Rs.100 and he receives only Rs.99 from customers so he is making loss
How much loss?
Long cut | Loss % formula =(100-99)/100 x 100=1% |
Shortcut | We assumed Rs.100 initially for the very reason that to prevent long cut formula! Since he receives one rupee less (100-99), his loss is 1%. |
In the actual exam, rough paper:
Invested | Received |
100 | 0.9 x 1.1 x 100=99 |
So, loss is 1%.
I hope the concept of marked price is clear by now. So it is time for a
MOCK TEST
Time: 20 Minutes
Correct =1m
Wrong= minus 0.33m
1. When Jethalal offers discount on cost price, he makes
- Profit
- Loss
- No Profit no Loss
- Profit or loss, depending on situation.
2. Jethalal’s offering to sell an LCD TV priced @Rs.1,79,299/- under two offers
- One time discount of 40%
- Successive Discount of 36% and 4%
Which offer is more beneficial from customer’s point of view?
3. Jethalal offered a scheme: “two successive discounts 10% and then 10%”. Which of the following scheme will give same effect?
- One time discount of 15%
- One time discount of 19%
- One time discount of 20%
- One time discount of 25%
4. Which of the following, is a better deal from customer’s point of view?
- Three successive discounts of 10,20,30%
- Two successive discounts of 20,20%
- One time discount of 50%
5. Jethalal offers two deals
- Successive discounts: first 10% and then 20%
- Successive discounts: first 20% and then 10%.
Which of the following are true?
- Customer will save more money in Deal 1
- Customer will save more money in Deal 1
- Customer will save same amount of money in both deals.
6. Jethalal fixes the sale price of his mobiles @15% above the cost price. He sells all his mobiles @12% less than the fixed price. What is his profit percentage?
- 2.5%
- 1.2%
- 1.5%
- 2%
7. Jethalal sells his mobiles on 10% discount on marked price. He bought a mobile @Rs.900 and wants to get 10% profit. What should be the marked price?
- 1275
- 1250
- 1175
- 1100
8. Jethalal wants to give 10% discount on all his mobile phones. But at the same time, he also wants to make 20% profit. At what percent above the cost price, should he mark the price of his phones?
- 25%
- 30%
- 33.33%
- 37.5%
9. Consider these statements
I. Marked Price is always higher than Cost price
II. Marked price is never lower than Selling price.
Which of above statements are correct?
- Only 1
- Only 2
- Both 1 and 2
- None
10. How can one become Master of aptitude?
- By searching for a competitive exam, that doesn’t have aptitude questions.
- By thinking like a loser, “My maths is not good and it can never be improved. I’ll just hope to clear some exam with luck by chance.”
- By watching India-England Cricket test series because those cricketers will give money to start some business, should you fail in the CSAT/IBPS/SSC/CMAT/CAT or some other stupid exam.
- By uploading motivational/funny photos on Facebook and tagging random friends in it.
- By practicing maximum questions at home.
Answers and Explanations
Q. | Ans. | Explanation |
1 | B | Discount on cost price=he’ll receive less money than his original investment=always loss. |
2 | A | 0.6<0.64×0.96 |
3 | B | Successive: 0.9×0.9=81 One time: 100-81=19 |
4 | C |
Customer has to pay minimum in situation “C”. |
5 | C | Order or sequence doesn’t matter in successive discounts. |
6 | B | Don’t be confused with vocabulary. Fixed price, marked price concept is same. 1.15×0.88×100 =101.2 Profit % is 101.2 MINUS 100=1.2% |
7 | D | Profit of 10% on 900=0.9 x Marked price MINUS 900 0.1*900=0.9*M-900 M=1100 |
8 | C | Assume cost price=Rs.100 Profit of 20% on 100=0.9 x Marked price MINUS 100 0.2*100=0.9*m-100 M=133.33 So marked price is 133.33-100=33.33% above the cost price. |
9 | C | Both statements are correct. |
10 | ?? | Lolz |
For the complete Archive of all aptitude articles, Visit Mrunal.org/aptitude
mrunal can u explain capital gains (n source to prepare topics like dese)
Capital gains is covered in vodafone article
https://mrunalmanage.wpcomstaging.com/2012/05/vodafone-essar-case.html
sir can u plz explain how to calculate the third proportional of two numbers
you are awesome… thankyou so much … :) ;)
Its grt fun :-) in markd price 4m profit dat equation can further b shortnd 1.125*800=0.9*M.P.
Thanks.Its grt fun :-) in markd price 4m profit dat equation can further b shortnd 1.125*800=0.9*M.P.
murnal kindly accept my eulogy for your simplification of the above problem . its encouraging that you have made aptitude a “cake walk”.
kudos to you
manish kumar
Eulogy is written for someone who has just died!! Anyways intention well taken. :)
“elegy” is a mournful poem for dead..Eulogy is right here..Anyways intention well taken..:)
You are right elegy is a mournful poem. but you may want to check Eulogy on google or any standard dictionary. Here am posting a link of wiki. http://en.wikipedia.org/wiki/Eulogy
you are right but eulogy means “high praise”..can be used for praising someone…just not meant for dead..:)
Partho is right.. Eulogy is ofcourse “high praise”.. But it refers especially to the high praises given during funeral and retirement.. So it is incorrect to use the word here by manish… Anyways intention well taken.. :-P
sorry i m interupting in this section…but plz can any1 tell me…wat govt reports we should refer to for upsc preparation….and if possible the websites etc from where to read
Isn’t the answer for question 9 = 2100, 10% profit of 900 is 990 (1.1*900)
I think you’re asking about Q7.
Jethalal invested Rs.900 and wants profit of 10%, after marking up price by 10%.
If he charges Rs.2100, he’d get profit of 133.33%. Answer wouldn’t match with the condition given in the question (10% profit).
thank u very much sir….waise in all Q 10 was a tough one…:)
nice satire on cricket watchers !
Sir, I have selected in SBI as assistant post. I am also preparing for civil services. Now as I will start earning I want to join coaching for the civil services preparation. But I am bit confused when I saw a large web of coaching names and brands in Mukherji nagar and Rajender nagar. So please suugest me a good coaching,my optional subjects are Geography and Public admins.
mrunal,kindly write on israel-hamas ceasefire.
Que-who will be benefited the most in this war?
i find many of us eulogizes our sir. but at the same time i wonder how can one ask accept my eulogy without any eulogy been writen.
sir
in Q no. 4 i got
a, 100-54=46
b, 100-36=64
c, 100-50=50
so in this case Rs 46 is d least where customer obviosly will benifit.
Please recheck multiplication done in option A.
Three successive discounts of 10,20,30%: leads to 50.4 and not 54
100 x 0.9 x 0.8 x 0.7=50.4
Thank you dear Sir :)
there was one question in a exam which held me spellbound, please answer this,
when we go to an apparel store and they say we offer you “Buy 3 and get 1” or other case “Buy 1 and get 3” what will be the overall discount???
discount=((MP-CP)/MP)*100
suppose MP=x
total MP=4x(sum of 4 MPs )
cost price=3x(you pay only for 3)
therefore,discount=((4x-3x)/4x)*100=25%
answer=25%
Thank u scientist!! topic clear now
Issac Newton>>>> Toooo much funy Yaar !!!
sir u really really explain very nice. u really these topics very simple otherwise earlier i was left only with calculating squares and cubes
A discount of 30% on the MRP reduces it SP by Rs 30. What is the new selling price ?
Please explain How to do it ? Will the ans be 70 ?
Here MRP is the SP.
Given 30% discount = Rs. 30
0.3*SP = 30
Therefore, SP = 100
New SP after discount = Rs. 70
if x + 1/x=3 then the value of x5+1/x5 is
if x^4 +1/x^4 = 23 then the value of (x-1/x)2 will be
Mrunal , Pls tell how to solve these types of questions .
(a+b)^2 = a^2 +2ab +b^2. In this case squaring both sides we get x^2 + 1/x^2 + 2(x)(1/x) = 3^2
thus x^2 +1/x^2 + 2 = 9 ; x^2 +1/x^2 = 7
Apply (a+b)^2 on x^2 +1/x^2 which gives x^4 + 1/x^4 = 47
Now go for (x^4 + 1/x^4) * (x+1/x) = 47 * 3 this will give x^5 + 1/x^5 + x^3 + 1/x^3
Value of x^3 + 1/x^3 can be calculated by (x^2 +1/x^2) * (x+1/x) and it comes out to be 60.
You final answer is 81.
Suppose,
A=(x-1/x)^2
or, A=x^2 1/x^2 -2*x*1/x
or, A 2 =x^2 1/x^2
or, (A 2)^2=(x^2 1/x^2)^2 (squre,both side)
or, (A 2)^2= x^4 1/x^4 2
or, (A 2)^2= 23 2
or, (A 2)= 5
or,A=3
sir ,please tell the strategy for ssc cgl tier 2?
An article is sold at a profit of 20%. If both the cost price and selling price are 100 less, the profit would be 4% more . find the cost price
Thanks, really helpful.
Q9. Marked price is always higher or equal to selling price
But Marked price and selling price may be less than cost price(in this case it is loss)
example
cost price is 100
selling price is 80(20% loss)
marked price is 88(10% discount)
statement is 1 is wrong in general and it is right only in case of profit
@Suresh…..
Any shopkeeper having a common sense of mind will like to sell for profit only because he also has to feed his children and food costs money. So, statement one is correct for all situations.
this is correct most of the times. but not all. if the stock is going unsold for a long time, the shopkeeper may sell it at a selling price/marked price slightly lower (but lower nonetheless) than cost price to attract customers and reduce his loss.
A shopkeeper marks on item 40% above the cost price and gives 15% discount to a customer. if the customer pays Rs 171 for the item what its cost price?
143.69
An article is sold at a profit of 20%. If both the cost price and selling price are 100 less, the profit would be 4% more . find the cost price
u knw d bst way 2 slve typo questions
is 2 use d options
cost price = 144
40% f cp means 144 + 57.6 = 201.6
15% discount on 201.6 = approx 171
you r just awesome…….
thank you so much for such a useful info…
MRUNAL SIR,
i wont be able to get question number 6….how 1.15*.88*100?
100-12/100 * 115=101.2
101.2-100=1.2
Its a very useful blog,n thanks MRUNAL SIR FOR THIS AWESOME WORK BY YOU.
sir;
i wante to buy mahesh misra’s arithmatics discriptive book . where will it be available. i searched via flipcart but i think there is not avilable.
it is very useful thankyou very much
ghatia sawaal hai badee.
Hello Admin,
Can you please tell me how to solve this sum??
2 candidates contested an election, 5% of the voters did not cast votes. The successful candidate won by 5100 votes, securing 48% of total votes. How many votes were cast for the elceted candidates?
a)239700
b)244800
c)484500
d)510000