Friday, October 31, 2014

Averages, Ratio & Proportion : A Few Tricks of The Trade

Tuesday, April 12, 2011, 17:00

Gone are the days when the “slow and the stea­dy” used to win the race, now it’s just the “fast and the furious” who snatch all the cakes and especially in the case of CLAT, you aren’t supposed be just ‘fast and furious’ but more importantly accurate!. In this short write up I would like to share with you some tricks which magically get rid of many lengthy and boring steps without affecting accuracy. In an examination like CLAT, which demands you to solve 200 questions in 120 minutes, which includes 20 maths questions for which you’re not expected to utilize more than 12-15 minutes (ideally), you need to be really fast. Now let me come to the point and share some tricks which can come handy for CLAT so as to enable you to do this section with full accuracy and this will certainly giveyou an edge.

Averages

This is certainly one of the most asked areas in CLAT and one should do this section thoroughly. Suppose there is a question where the average weight of a class consisting of 20 students is 40 kilograms and if a teacher is added then the average increases by 2 kgs. Now such questions are very easy but by using a short cut method, it turns out to be extremely easy.However, always remember that the tricks are also steps in themselves, so practice a lot before you actually use them, so that you improve your overall efficiency.

Now, in questions like this one, just multiply the new number. of people in class, i.e. 21 with old average weight, i.e. 40. The product is 840. Then, multiply increase in average weight with new no. of people in class, i.e. 21. Your equation should be like 21 X 2 = 42. Now add previous product and this product, here is you answer, i.e. 840 + 42 = 882.

Ratio and Proportion

I When A : B = m : n, and B : C = p : q. Then A : B : C = mp : pn :nq.

Such questions are also widely asked in examinations like CLAT, so make sure that you don’t mug up such rules but your mind should absorb and internalize such tricks.

II When A : B = m : n, B : C = p : q, and C : D = r : s. Then A : B : C : D = mpr: npr : nqr : nqs.

Try to find a particular pattern being followed in both the tricks so that you don’t haveto memorize the equation.

Explanation: i) A : B = 1 : 2

ii) B : C = 3 : 4

iii) C : D = 5 : 6

Then A : B : C : D = 1*3*5 : 2*3*5 : 2*4*5 : 2*4*6

And, A : B : C : D : = 15 : 30 : 40 : 48

III Suppose there are two containers and in one container, oil and water are in ratio p : q and in other container oil and water are in ration r : s. Now if both the containers are emptied in a third container then in third container the ratio between oil and water will be:


{ p/p+q + r/r+s} : {q/p+q + s/r+s}

Explanation: If there are two containers and in one container oil and water are in ration 1: 2, and in second container oil and water are in ration 1: 3. Now both the containers are emptied in a third container, then the ration of oil and water in the third container will be: 1/(1 + 2) +1/(1 + 3) : 2/(1 + 2) + 3/(1 +3)

Now, it comes like 1/3 + 1/4 : 2/3 + 3/4

= 7/12 : 17/12

=7 : 17.

IV The shortcut under this head is very important as it saves a lot of time, and moreover these type of questions are frequently asked in examinations like CLAT. Now, suppose that in a container the ratio between oil and water is p : q and the quantity is x litres. And now if you have to find the amount of water to be mixed so that the ratio becomes a : b, then it can be solved by following method:

x(pb – qa)

a(p + q)

Explanation: In a container there is 40L mixture of milk and water, which are in the ration 3:1. How much water is to be mixed to make the ration 2:1.

Now: 40(3*1 – 2*1) =40(1) = 40 = 5L

2(1 + 3) 4*2 8

I will reiterate the same thing again that these formulae are not for mugging up but these need to be practised enough number of types so that you know the basic funda working behind it and moreover if you are still not able to absorb it you want to cram then first of all change the each formulae in such a way that each formula has different set of alphabets used in it otherwise the pressure of CLAT will make you to mess it up. Now, good luck to all of you and we will try to come up with new time saving tricks so that you people have better chances of making it through.

Again good luck.
Shubhank Sanjeev,
NALSAR University of Law.

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33 Responses to “Averages, Ratio & Proportion : A Few Tricks of The Trade”

  1. Adithya Reddy said on Wednesday, April 13, 2011, 8:27

    These shortcuts are really useful(especially for a guy like me who’s weak at maths)…thanks a TON!!!! :D

    Reply

  2. Tathagat said on Wednesday, April 13, 2011, 8:34

    Explanation: In a container there is 40L mixture of milk and water, which are in the ration 3:1. How much water is to be mixed to make the ration 2:1.
    Now: 40(3*1 – 2*1) =40(1) = 40 = 5L
    2(1 + 3) 4*2 8

    -I didn’t understand how the last bit of it worked. I mean, what are we supposed to do with the new 5L figure? More importantly, what exactly is it? Also, how did you find ‘ 2(1+3) ‘ ?

    Thanks

    Reply

    Anchit Reply:

    The formula is : x(pb – qa) / a(p + q).

    ‘2(1+3)’ came from a(p+q) .

    The new 5L is the amount of water you need to mix ie. the answer.

    Reply

    Dhatterika ! Reply:

    It is 40 (3-2)/ 2(1+3) = 40/8 = 5 ( WHAA !! Apply some sense ! )

    Reply

  3. Saumya said on Wednesday, April 13, 2011, 9:50

    Thanks a lot for this! :)

    Reply

  4. manasa said on Wednesday, April 13, 2011, 9:59

    thank you.was really helpful.

    Reply

  5. puja rajput said on Wednesday, April 13, 2011, 10:21

    thank u so much fr diz wonderflu time saving tricks….its really very helpful in solving such probles n also minimise chances of makig calculation mistake tat we generally make in following those mrthods

    Reply

  6. lipika said on Wednesday, April 13, 2011, 12:37

    always had trouble getting the answers in time….thank u for the shortcut method:-D

    Reply

  7. Vishal said on Wednesday, April 13, 2011, 12:50

    Thanks!

    Reply

    rajeev kumar Reply:

    thank u so much. these techniques are very usefull in verious compitition and in very short time we can score very good marks. and achived our goal………. thank’s regards .

    rajeev kumar

    Reply

  8. Anchit said on Wednesday, April 13, 2011, 16:57

    Nice tips, thanks CG >.<

    Reply

  9. deepan shah said on Wednesday, April 13, 2011, 18:19

    there is a mistake in the first sum 21*40=840 & not 440.
    due to this the ans in the end is also wrong

    Reply

    Asad Reply:

    Was a typo. Corrected. Thanks.

    Reply

  10. Virath said on Wednesday, April 13, 2011, 18:47

    can u give us some tricks on work , time -distance , questions it takes a hell lot of time esp no of days required 2 do a certain piece of work. etc

    Reply

  11. Aadhya said on Friday, April 15, 2011, 18:06

    Uuuuhhh… Now what’s with this timer on CLAT? Eeeee…. Freaks me out..

    Reply

    Asad Reply:

    It does? . That means that its purpose is solved!

    Work work!! :D

    Reply

    Saumya Reply:

    The very Obvious purpose. Uhh. :)

    Reply

  12. Adarsh said on Thursday, April 21, 2011, 0:10

    pls give us some mor wonderful shortcuts like these….it will really ease the pressure on the students

    Reply

  13. puneet said on Monday, July 4, 2011, 19:34

    do u mathematically prove” When A : B = m : n, B : C = p : q, and C : D = r : s. Then A : B : C : D = mpr: npr : nqr : nqs.????”

    Reply

  14. Gaurav said on Sunday, October 16, 2011, 13:12

    Thanks……..

    Reply

  15. shubhangi jaiswal said on Sunday, March 11, 2012, 23:47

    thanx a lot… these r really helpful

    Reply

  16. aprajita said on Sunday, April 29, 2012, 18:22

    thnks a lot..these triks r realy vry helpful…:)

    Reply

  17. roymisgbs said on Monday, May 7, 2012, 11:56

    WTHELL the solution can be achieved much faster in the case of the 40 l mil and water problem …
    40 l mixture … ration 1:3 ==> 10 litre water and 30 litre milk ==> add 5L water to make it 30/2 … hence solved
    the other methods save a lot of time i agree

    Reply

  18. Shubangi said on Monday, May 7, 2012, 12:34

    Thank you all a lot, Asad and team for helping us out… there are 6 days left for CLAT, and I hope I’ll make it…:-)

    Reply

  19. harshit said on Friday, May 11, 2012, 1:03

    u guys r real legends..
    thnx..thnx alot

    Reply

  20. Priyanka said on Thursday, August 16, 2012, 7:47

    You guys are awesome :) Thanks for all the help!!

    Reply

  21. vivek said on Friday, November 2, 2012, 15:53

    can u give shortcut for if a:b=2:3 , b:c=6:7 , c:d=14:25 then find a;b;c;d ?
    thnks in advance

    Reply

  22. preeti said on Wednesday, February 6, 2013, 14:54

    thanks

    Reply

  23. vikas sharma said on Friday, February 8, 2013, 16:04

    give tricks for the question of coins ..ie coins denomination then calculate no. of coins

    Reply

  24. santosh paswan said on Saturday, August 17, 2013, 1:14

    thanks sir

    Reply

  25. mynk said on Thursday, December 5, 2013, 15:42

    5.

    In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is:

    Reply

    Swarnima Reply:

    60L. Refer – roymisgbs answer above for the calculation.

    Reply

  26. Dinesh said on Thursday, December 26, 2013, 11:34

    These are very complex and hard to understand.

    Reply

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