- 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 |
- 0.9*0.8*0.7=0.504
- 0.8*0.8=0.64
- 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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