[Aptitude] Long Division, Two-Digit Division, % Calculation Without Tears (and Without Boring Vedic...

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[Aptitude] Long Division, Two-Digit Division,% Calculation without Tears (and withoutboring Vedic Maths) using % ApproximationMethod

Ok this isn’tabout boringvedic mathstechnique sodon’t run away,yet!

One of thebiggestproblemwithIBPS/Bank,SSC, CAT, CMAT type of exams= you’ll encounter

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1 of 15 6/12/2014 3:59 PM

long division and percentage (%) calculation everynow and then, directly or indirectly (in Datainterpretation questions).And If you’re not good with speed maths, you’llwaste a lot of time in such stupid calculations.

For the the aptitude questions of Bank/MBA exams,Knowing the answer approach is not sufficient. Youalso need to get the answer quickly and accurately.Otherwise someone else will tick more answers andhe’ll get the rank.

Consider these two questions

Question

In a warehouse there

are 230kg of wheat

initially. But rats ate

away 34 kg. How

much % of wheat is

left?

What is the

answer of

196/23=?

Answer

49.3%1.

60.1%2.

85.2%3.

85.7%4.

4.931.

6.012.

8.523.

8.574.

Approach

{(230-34)/230}

x100=(196/230)x

100=answer

196/23= answer

Everyone, even with half hearted preparation, knowsthe approach. But The problem is actually in ‘doing’that calculation or division (196/23). Here I’ll show asingle method, to solve both type of calculations. As

Objective...

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2 of 15 6/12/2014 3:59 PM

long as you know how to add two numbers, and howto multiply a number with 5, you can execute thismethod effortlessly.

First create a “Master Table” (don’t just read it, dothis simultaneously using your own pen andpaper)

100% 230

Now make a new row for 50%

100% 230

50%

So either divide 230 by 2=115or multiply 230 with 5 and then shift one decimalpoint leftwards. (that is 1150 ==> to 115.0)In either case you get 50% of 230=115

100% 230

50% (half of 230) 115

Now make a new row for 20% but keep it empty rightnow.

100% 230

20%

Create one more row for 10% and simply shift onedecimal leftwards. i.e. 230–> 23.0

100% 230

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3 of 15 6/12/2014 3:59 PM

50% (half of 230) 115

20%

10% (one decimal point less) 23.0

Now double the 10% number (i.e.by adding 23 into 23again) so you get 23+23=46. That’s our 20%. Fill up thetable.

100% 230

50% (half of 230) 115

20% (double of 10%) 46

10% (one decimal point less) 23.0

Our master table is ready, now Imagine there is a bigwater tank with total capacity of 196 lit.

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है !

U PS C

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4 of 15 6/12/2014 3:59 PM

We can fill it with buckets of size 10%, 20% and 50%only.We want to fill up the tank with minimum effort. Sofirst take 50% (115), some space will be left.By this time you get the idea that

answer is more than 50% (if % value of 196/230 isasked)

1.

answer is more than 5 (if absolute value 196/23 isasked)

2.

so eliminate answer options that donot meet thesecriteria.

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5 of 15 6/12/2014 3:59 PM

Move on

Tank Filled Buckets

196 115 50%

Total 115 50%

There is still some space left in the tank so let’s throwa 20% bucket

Tank Filled Buckets

196 115 50%

046 20%

Total 161 70%

Or you can add 10% bucket two times, you’ll get sameresult.

It’s clear that our answer is bigger than 70%. Soeliminate any options less than 70%

Hmm, so far we’ve filled 161, It can still accommodateanother 10% bucket

Tank Filled Buckets

196 161 70%

023 10%

Total 184 80%

Now we are very close, only 196-184=12 lit. remains.But no bucket is that small!

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6 of 15 6/12/2014 3:59 PM

Solution= move the decimal numbers, to create newsmall sized buckets.

Master TableMoving decimal

numbers

100% 230

50% (half of 230) 115 5% 11.5

20% (double of 10%)23×2=

462% 4.6

10% (one decimal point

less)23.0 1% 2.3

In the exam, you don’t have to actually write newcolumns of 5%, 2% and 1%, just visualize them in yourhead, by shifting the decimal to one point leftwards.

Recall that 12 lit is empty and Now we’ve a new 5%bucket that can almost fill it up.

Tank Filled Buckets

196 184 80%

011.5 5%

Total 195.5 85%

By this time you get the idea that

answer is just a little higher than 85% (if % of196/230 is asked)

1.

answer is just a little higher than 8.5 (if absolutevalue 196/23 is asked)

2.

so eliminate any answer options that are not meeting

S p ec i a l i s t

M e di ca l /A l l ie d

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7 of 15 6/12/2014 3:59 PM

this criteria.

Still if two or more options remain. For example

8.521.8.572.

^This situation usually happens in CAT DataInterpretation questions. Now what to do?

Well, Total capacity is 196 lit. and so far we filled up195.5 so, 0.5 lit is still empty. But no bucket is smallenough to carry water in this scale. Solution= createmore buckets, by shifting decimal points in the“Master Table”.

Master TableMoving decimal

numbers

100% 230 Phase I Phase II

50% (half of 230) 115 5% 11.5 0.5% 1.15

20% (double of 10%)23×2=

462% 4.6 0.2% 0.46

10% (one decimal point

less)23.0 1% 2.3 0.1% 0.23

Recall that 0.5 lit is empty and from above table, it isclear that 0.2% bucket (0.46 is very close) so let’s useit.

Tank Filled Buckets

196 195.50 85%

000.46 0.2%

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8 of 15 6/12/2014 3:59 PM

Total 195.96 85.2%

So the final answer is

196/23=8.52196/230=85.2%

If you want even more accurate answer, create morebuckets and proceed in the same manner.

Important sidenotes

Whenever you have to do long-division e.g.256/29, always make the denominator (bottomnumber i.e. 29) very close to the top number (256)and take that as 100%. That is 290=100%. And thenrephrase question: “256 is how much % of 290”,then proceed according to the method you justlearned. You’ll get 88.27%. but our question was256/29. Recall that you’ve added one zero more.(290)

1.

So, 1%=1/100

Therefore, 88.27%=(88.27/100)

And from the ‘bottom’ we take back one zero that wehad added earlier. So instead of 100, there remainsonly 10

88.27/10=8.827 is our answer for 256/29

If there is 7526/67 then? Again same method, 7526is how much % of 6700? You’ll get 112.3%. this timewe’ve added two zeros more (i.e.we used 6700instead of 67).

2.


9 of 15 6/12/2014 3:59 PM

So, 1%=1/100

Therefore 112.3%=112.3/100

But take back those two zeros we had added earlier.So, instead of 100, there remains only 1

112.3/1=112.3 is our answer for 7526/67

This method looks awkward and tiresome initially,but once you’ve enough practice of doing mentaladdition then it’s way easier than the Vedic Maths’concept of double or triple digit division (becausein Vedic method, many a times you’ve to adjustand carry over the numbers= notvery convenient).This method can be used for three-digit, four digitdivisions also.You can do any division as long as you can findout 10%, 20% and 50% of a number (andconsequently 1%, 2%, 5%, by shifting decimalplaces.)

Applications of ^this method

Percentage calculation or Long Division has direct orindirect applications in following topics:

Profit Loss1.Data Interpretation, especially those based onPie-charts.

2.

Compound interest, Simple Interest Rate,Population Growth: by the way, they can be solvedwithout mugging up formulas, click me to knowhow!

3.


10 of 15 6/12/2014 3:59 PM

Mixture-Alligiation, Wine-water, Metal alloys: canbe solved without mugging up formulas, clickme to know how!

4.

Time-Speed-Distance, Time and Work, Pipes andCisterns, Boats and Railways. All of them arebased on the STD formula: speed x time =distance. So there is almost always a situationwhere two variables are given and third is to befound= division. All of them can be solved bymugging only single STD formula. Techniques arescattered around on this page:Mrunal.org/aptitude

5.

Test your skill

Question %Absolute

ValueHint: 100% is

231/19 190

181/29 290

158/117 117

198/6767 (because 670 would be too

far)

67/51 51

51/29 29

158/117 117

8189/541 5410

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joe 30/04/2014 at 12:05

Reply

good effort.. thnks!!

miku 24/05/2014 at 07:32

Reply

thanku sirji…..this post really helpful


13 of 15 6/12/2014 3:59 PM

‹ पुरानी कम स 1 2

Rc983 09/06/2014 at 20:29

Reply

nice approach ,thanks for post . i never liked vedicmaths etc btw.

अपना कमट नीचे ल खए!

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[Aptitude] Long Division, Two-Digit Division, % Calculation Without Tears (and Without Boring Vedic...

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