 [Aptitude] Percentage: X% of Y is same as Y% of X. ~ RAVI MOHAN MISHRA

## [Aptitude] Percentage: X% of Y is same as Y% of X.

Nowdays, there is very high competition in all examinations, So merely knowing all the concepts is not going to take you through examination, There is a need to solve the Questions quickly, it comes through some tricks and lot of practice.This article will help you in solving some percentage questions quickly.

Percentage to Fraction Conversion

Let us Begin:

Statement: Is X% of Y same as Y% of X ?( pause for a moment and think, then proceed)

Let us verify above statement.

X% of Y = X/100 * Y= X*Y/100  -- (1)

&

Y% of X = Y/100 * X= Y*X/100  -- (2)

So, From equation 1 and 2 it is clear that X% of Y has exactly same value as Y% of X.

The above statement reduces our calculation in many percentage problems. Let us take an example.

Ques: Calculate 32 % of 50.

Solution:  Since we know, X% of Y and Y% of X are same.

So, 32% of 50 = 50% of 32.

Now there is nothing left to calculate as you all know,

50% = 1/2

So, 50% of 32= 1/2*32= 16.

If you are good in converting percentage into fraction, and you know that X% of Y is same as Y% of X.You can easily reduce calculation in many percentage problems.

Summary Always try to use the relation X% of Y= Y% of X. Through practice you can master your brain, which will automatically convert it, and calculation will become easier for you.

Let us try another problem.

Ques: what is  the value of
45% of  280 + 28% of 450.

Solution
:  Any one can solve above expressioni, But our purpose is to solve it quickly.

Look at the second term,

28% of 450 can be written as 45% of 280. ( those who doubt everything can solve and varify)

Now, our expression becomes,

45% of 280 + 45% of 280= 90% of 280= (100% of 280)-( 10% of 280)= 280-28= 252 Ans.

( fraction equivalent of 100% =1 & fraction equivalent of 10% =1/10)

Question: 42% of  250 + 12.5% of 840.
Solution
:
In this question it does not look directly that here we can apply X% of Y = Y% of X.

Look at the second expression.

12.5% of 840 = 25% of 420 ( as 25% of 100 is same as 50% of 50)

Now our expression becomes.
42% of 250 + 25% of 420

Since 42% of 250=25% of 420.

So, 42% of 250 + 25% of 420= 25% of 420 + 25% of 420 = 50% of 420 = 1/2* 420 = 210 Ans.

Now its your turn, Solve few mock Questions.. Try to do all the questions mentally without using pen, if it does not get solved mentally then only use pen & paper.

Mock Questions

Q1) 68% of 25 = ?

A] 15
B] 16
C] 17
D] 18

Q2) 38% of 50 = ?

A] 16
B] 17
C] 18
D] 19

Q3] 55% of 460 + 46% of 550=?

A] 414
B] 424
C] 496
D] 506

Q4) 48% of 400 + 20% of 960= ?

A] 364
B] 384
C] 416
D] 436
Enroll for Online Courses By RaMo (99.99%iler CAT)  and give A boost to your preparation. 1. Excellent Article! Keep up the good work, Ravi!!!!

1. Thanks for the feedback Chetan.. Keep visiting :)

2. wonderful.....thanks ravi

1. Hello Yash... Keep visiting ...
more articles to come.

3. whr r ans???

1. Hi Yash,
I do not give answers so that everyone try to solve the problems. Answers are
1.C
2.D
3.D
4.B

4. So nice, i'm enriched... Thanks Ravi

1. You are welcome, keep visiting for more articles. Good Luck 😊 www.facebook.com/mishraravimohan

5. So nice, i'm enriched... Thanks Ravi

6. jabarjast hai ravi........................

7. Sir,can u give example for above same for 78.9% 789?? how to solve this kind quetions?

1. Hello Hetal,
Let us take an question:
78.9% of 250 + 25% of 789=?
Use x%y = y%of x =>
78.9% of 250 = 25% of 789.
So, expression = 50% of 789 = 1/2*789 (since 50%=1/2).
= 394.5 and.

Let us take another question.

78.9% of 555 + 55.5% of 789 = ?
Use x% of y = y% of x.

Expression = 111% of 789 => now calculate like this.
111% of 789 = (100%+10%+1%) of 789= 789+78.9+7.89 = 875.79 answer.

Hope its understood :)
Good Luck :)

8. Thanks a lot Sir..:)

9. wow!!! great

1. Hello Sameer,
Good Luck:)

10. very nice work sir......i saw your articles very late dats my fault....otherwise would have cracked something bigger this time .....but i am happy I found your blog ...ty for your true efforts

1. Hi Sourabh,
Good to hear these articles are helping you in your preparation.
Will keep writing regularly now onwards,
Keep Visiting.
Good Luck :)

11. thank u sir

12. hllo sir...u r really grt guider of thousands of students.....before reading ur articles, im vry confused in the concepts of PERCENTAGE....but after redngg ur articles, im damn sure confidence on myslf.....
sir i hvv a confusion in" examination,(max.marks,least marks,boys,girls) related Percentage problms"...plzz do write articles on tht so thr will b no confusion....

13. grt article sir 👍

14. nice ! very valuable

15. Ravi sir ... :) can uh plss suggest some ways to.increase speed... :) and also how to.solve di in min time...

1. call us @8860435969.

16. 29.8% of 260+ 60.01% of 510 -103.57
Through approximation. Can v use same strategy in approximation.

1. Yes, it can be used anywhere
29.8% of 260 + 60.01% of 510 = 26% of 298 + 51% of 600.1 ~

(25% + 1% ) of 298 + ( 50% + 1% ) of 600.1 => Now use 25% = 1/4 and 50% =1/2

=> 1/4 x 298 + 2.98 + 1/2 x 600 + 6 => 74.5 + 2.98 + 300 + 6 = 383.03

Final expression => 29.8% of 260+ 60.01% of 510 -103.57 = 383.03 - 103.57 = 379.46 (approx)
Hope you understand.

Cheers,
RaMo

17. sir how u have solved the last mock question plzz explain ????

18. Dear sir, pls help
How come there 111 ?? 111% of ??
Thanks

Let us take another question.

78.9% of 555 + 55.5% of 789 = ?
Use x% of y = y% of x.

Expression = 111% of 789 => now calculate like this.
111% of 789 = (100%+10%+1%) of 789= 789+78.9+7.89 = 875.79 answer.

1. 78.9% of 555 + 55.5% of 789 = ?
55.5% of 789 + 55.5% of 789 => since 78.9% of 555 = 55.5% of 789
111% of 789
Expression = 111% of 789 => now calculate like this.
111% of 789 = (100%+10%+1%) of 789= 789+78.9+7.89 = 875.79 answer.

Hope its understood :)
Good Luck :)

19. Dear sir, still i've not understood ^

u have not said anything new to make me understand. i mean HOW COME 111 ? FROM WHERE ? taking 111% directly how ? pls explain only about 111, rest i've understood.

20. what a bingoooo.........hats offf

but sir I didn't understand the 78.9% 789??kinda question which is asked by hetal can you plz explain it

21. 22. 78.9% of 555 can be represented as 55.5% of 789.
HOW!?=>
(78.9/100 of 555) equivalent to (555/100 of 78.9) that again is equivalent to (555/100 of 789/10) equivalent to (555/1000 of 789) equivalent to (55.5/100 of 789) equivalent to (55.5% of 789).. got it..
..And after that ...we multiply the whole expression with two..as we now have addition b/w the two identical expressions..so by this we get 111 (55.5 multiplied by 2=111.0)

Thanks,
Hope I was of some help.
I just visited today for the first time.
Awesome content.
Thank you Sir.
:)

23. Excellent !!

24. solve this ..... and plz tell how to solve this.....
x% of y = 50 then y=?