[Aptitude] Concepts of Marked Price and Successive Discounts (Profit-Loss) without (stupid) formulas

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M K Yadav IAS Coaching
Profit, Loss, Discount, Marked Price = all of them are mere extension of Percentage calculation concept. And they can be solved effortlessly, without mugging up any formulas.
  1. What is Discount?
  2. What is successive discount?
  3. Case: Successive vs One Time Discount?
  4. What is marked price?
  5. Case: Finding Marked Price from Profit %
  6. Case: Finding marked price from Selling price
  7. Case: Finding % Profit / loss in MP-Discount
  8. MOCK TEST
  9. 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?
Concept: Successive Discounts

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

  1. Rs.1,320
  2. Rs.1,350
  3. Rs.1,360
  4. 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

  1. Buy it at one time discount of 30%
  2. 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:
Concept Marked Price, DiscountMind 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?

  1. Rs. 1,000
  2. Rs. 1,100
  3. Rs. 1,200
  4. 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?

  1. Rs.11
  2. Rs.44
  3. Rs.33
  4. 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. 1% profit
  2. 1% loss
  3. 5% profit
  4. 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

  1. Profit
  2. Loss
  3. No Profit no Loss
  4. Profit or loss, depending on situation.

2. Jethalal’s offering to sell an LCD TV priced @Rs.1,79,299/- under two offers

  1. One time discount of 40%
  2. 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?

  1. One time discount of 15%
  2. One time discount of 19%
  3. One time discount of 20%
  4. One time discount of 25%

4. Which of the following, is a better deal from customer’s point of view?

  1. Three successive discounts of 10,20,30%
  2. Two successive discounts of 20,20%
  3. One time discount of 50%

5. Jethalal offers two deals

  1. Successive discounts: first 10% and then 20%
  2. Successive discounts: first 20% and then 10%.

Which of the following are true?

  1. Customer will save more money in Deal 1
  2. Customer will save more money in Deal 1
  3. 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?

  1. 2.5%
  2. 1.2%
  3. 1.5%
  4. 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?

  1. 1275
  2. 1250
  3. 1175
  4. 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?

  1. 25%
  2. 30%
  3. 33.33%
  4. 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?

  1. Only 1
  2. Only 2
  3. Both 1 and 2
  4. None

10. How can one become Master of aptitude?

  1. By searching for a competitive exam, that doesn’t have aptitude questions.
  2. 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.
  3. 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.
  4. By uploading motivational/funny photos on Facebook and tagging random friends in it.
  5. 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
  1. 0.9*0.8*0.7=0.504
  2. 0.8*0.8=0.64
  3. 0.5

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

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112 Comments on “[Aptitude] Concepts of Marked Price and Successive Discounts (Profit-Loss) without (stupid) formulas”

  1. formula for 2 successive discount formula if successive discounts given are a & b, then total discount is
    a + b – (ab/100)

    Shortcut formula for 3 successive discount formula if successive discounts given are a, b, c then total discount is
    a + b + c – (ab/100 +bc/100 + ca/100 – abc/10000)

  2. X purchase an item28,000 by getting a discount of20% on the marked price which is175% of the cost price,but still earned a profit of12%,what is the costprice

  3. Mr. Rishh, jo apne ram bhai k discount wale sawal ka answer diya hai usme mera aur apka sirf mp hi match kar raha hai but cp to mera match nahi kar raha kya aap isk detailed sol denge please.
    Your cp : 720
    My cp : 2000

  4. Ravish lost 20% by selling a radio set for 3072/-. What percent will he gain by selling it for 4080/-.

  5. Find the CP when SP is 200/- and loss is 35%.?

  6. Can I marked a article MPR rs 900. But actual purchase of RS. 125 and sale price 150

  7. The discount % on 3 articles a:b:c is 10%,20%,25% and the ratio of no. of articles is 1:2:4 and sold ratio of a:b:c is 2:5:5 . Find the overall discount % on the total selling of articles? Please help to solved.

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