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.

35 COMMENTS

  1. 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

  2. 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

    • 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

  3. 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.????”

  4. 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

  5. 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…:-)

  6. 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:

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

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