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

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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.

1. Adithya Reddy

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

2. Tathagat

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

• Anchit

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.

• Dhatterika !

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

3. Saumya

Thanks a lot for this! 🙂

4. manasa

thank you.was really helpful.

5. puja rajput

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

6. lipika

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

7. Vishal

Thanks!

• rajeev kumar

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

8. Anchit

Nice tips, thanks CG >.<

9. deepan shah

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

• Was a typo. Corrected. Thanks.

10. 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

11. Aadhya

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

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

Work work!! 😀

• Saumya

The very Obvious purpose. Uhh. 🙂

12. Adarsh

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

13. puneet

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.????”

14. Gaurav

Thanks……..

15. shubhangi jaiswal

thanx a lot… these r really helpful

16. aprajita

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

17. roymisgbs

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

18. Shubangi

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…:-)

19. harshit

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

20. Priyanka

You guys are awesome 🙂 Thanks for all the help!!

21. vivek

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

22. preeti

thanks

23. vikas sharma

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

24. santosh paswan

thanks sir

25. mynk

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:

• Swarnima

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

26. Dinesh

These are very complex and hard to understand.

27. mohan

it is fantastic website

28. RISHABH SRIVASTAVA

Nice BT if we will start memorizing maths concepts,then it will be a shame on us especially science stream guys.

29. Vinod dadhich

Very good

30. simran

😀

31. Kasvi

Hey I have a query. The fourth method talks about the quantity of water that needs to be added, if the same question was rephrased as: old ratio of oil and water in a mixture of 40l being 2:1 and new one to be 3:1, what quantity of oil needs to be added, would we interchange the p and q in the formula?