Percentages - Absolute Basics

Today's article will deal with some basics of percentages that can be implemented in DI section as well its application areas of Profit, Loss & Discount(PLD) ; Simple and Compound Interest(SI_CI) and the like which I will be presenting soon as a follow up to this article. So let's start!
The above presented table would prove really helpful to you in several sections of Quantitative aptitude and Data Interpretation. Basically it would help you wherever you deal with numbers and percentages. PLD,SI_CI as well as in Time and Work problems if you are accustomed to the efficiency approach. Moreover, DI problems involving %ages would definitely deal with these numbers. So first things first, learn and keep this handy with you to keep revising it till they are on your fingertips.


Concept 1:

Then, I would like to talk about the data interpretation calculation tips in the context of using percentages as a tool. Let's call this a 10% rule for DI.
Let's see what this is all about..

Simple data table :
5 students : A,B,C,D,E give 3 exams P,Q,R which have total marks as 120,200 and 250 respectively.
Let's consider student A. His scores are 34%, 68% and 45.4% in P,Q,R respectively and similar data is provided for all 5 students. You are asked to find the subject wise and overall topper and second place student of the class assuming there are only 5 students in the class [else answer would cannot be determined]

How do you think you'll find 5*3 = 15 individual %age calculations and save time?

Let's unveil the 10% rule now.

10% of a number pq.xyz means moving the decimal one place to the left : p.qxyz
1% means moving it two places to the left : .pqxyz
and 0.1% means moving it three places : .0pqxyz

Using this for our task :

A scores 34% marks in P(total : 120)
34% = (30 + 4)% = 3*(12) + 4*(1.2) = 36 + 4.8 = 40.8 <= Did you see what happened there? 

Let's do this thing one more time..
 
A scores 68% marks in Q(total : 200)
68% = (70 - 2)% = 7*20 - 2*2 = 140 - 4 = 136 <= How about now? Are you getting how it's done.

3 times' the charm..

A scores 45.4% marks in R(total : 250)
45.4% = (40 + 5 + 0.4)% = 4*25 + 5*2.5 + 4*0.25 = 100 + 12.5 + 1 = 113.5
 
I hope next time you see such figures you'll not start with seeing them as fractions and dividing strange figures(well it might be useful at times actually. But that's your observation)
 

Concept 2:

Another place to use this is while comparing ratios..
123/140 , 115/213 , 110/124..

Find what % of 140 is 123 coming out to be and same for rest.
Smart thing to do here would be to put 115/213 as the smallest[try to figure out why..simple ratio rules..Leave comments if you don't get it still]

140 : 10% = 14 , 1% = 1.4 , 0.1% = 0.14
You try going as near as possible depending on the closeness of ratios.
123 ~ 112 + 9.8 + 1.12 = (80 + 7 + 0.8)% = 87.8%

124 : 10% = 12.4 , 1% = 1.24 , 0.1% = 0.124
110 ~ 99.2 + 9.92 = Already 88. something hence greater than 123/140.


Final order : 115/213 < 123/140 < 110/124

Concept 3:
 
Let's see one final important concept in percentages that has widespread applications in PLD,SI_CI,etc..successive percentage change.


A quantity is increased by 10% and then the changed value is dropped by 4% [Sensing something of the profit loss discount scenarios? ]. What is the net % change from original cost?

Say, quantity is X. You increase it by 10% => X' = X + X*10/100 = X(1 + 10/100)

Now this quantity X' is decreased by 4% => X" = X' - X' * 4/100 = X'(1 - 4/100)
 
= X(1 + 10/100)(1 - 4/100) and some things start to look like our compound interest..
= X(1 - 4/100 + 10/100 - 10*4/10000) = X[1 + ((a - b - ab/100)/100)]
= A net change of (a - b - ab/100) %

So the general formula for two successive % change = a + b + ab/100 as the net % change over the original quantity with appropriate signs for a rise(+ve) and drop(-ve).

 
Since you know the concept now..try discovering what it would have been for three successive % change :)

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Until next time..
Cheers!
AS