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

Tuesday, 11 February 2014

[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.

For understanding this article knowledge of percentage to fraction conversion is required, if you have not read it by now please click on the link below:

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

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34 comments:

  1. Excellent Article! Keep up the good work, Ravi!!!!

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

      Delete
  2. Replies
    1. Hello Yash... Keep visiting ...
      more articles to come.

      Delete
  3. Replies
    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

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

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

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

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

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

    ReplyDelete
    Replies
    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 :)
      Do reply :)
      Good Luck :)

      Delete
  8. Replies
    1. Hello Sameer,
      Good to hear you found this article useful.
      Read all other articles too.
      You can connect with me on my Facebook page & you can ask your queries.
      Do share this article with your friends.
      Good Luck:)

      Delete
  9. 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

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

      Delete
  10. 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....

















    ReplyDelete
  11. nice ! very valuable

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

    ReplyDelete
    Replies
    1. call us @8860435969.
      We would be happy to help you.

      Delete
  13. 29.8% of 260+ 60.01% of 510 -103.57
    Through approximation. Can v use same strategy in approximation.

    ReplyDelete
    Replies
    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

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

    ReplyDelete
  15. 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.

    ReplyDelete
    Replies
    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 :)
      Do reply :)
      Good Luck :)

      Delete
  16. 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.

    ReplyDelete
  17. 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

    ReplyDelete
  18. Very helpful articles....Thanks alot

    ReplyDelete
  19. 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.
    :)

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

    ReplyDelete