mrunal [aptitude] long division, two-digit division, % calculation without tears (and without boring...

[Aptitude] Long Division, Two-Digit Division, % Calculation without Tears(and without boring Vedic Maths) using % Approximation Method

Ok this isnt about boring vedic maths technique so dont run away, yet!

One of the biggest problem with IBPS/Bank, SSC, CAT, CMAT type of exams=youll encounter long division and percentage (%) calculation every now and then,directly or indirectly (in Data interpretation questions).And If youre not good with speed maths, youll waste a lot of time in such stupidcalculations.

For the the aptitude questions of Bank/MBA exams, Knowing the answer approach isnot sufficient. You also need to get the answer quickly and accurately. Otherwisesomeone else will tick more answers and hell get the rank.

Consider these two questions

QuestionIn a warehouse there are 230kg of wheat initially. Butrats ate away 34 kg. How much % of wheat is left?

What is theanswer of196/23=?

Answer

49.3%a.60.1%b.85.2%c.85.7%d.

4.93a.6.01b.8.52c.8.57d.

Approach {(230-34)/230} x100=(196/230)x 100=answer 196/23= answer

Everyone, even with half hearted preparation, knows the approach. But The problem isactually in doing that calculation or division (196/23). Here Ill show a single method,to solve both type of calculations. As long as you know how to add two numbers, andhow to multiply a number with 5, you can execute this method effortlessly.

First create a Master Table (dont just read it, do this simultaneously using yourown pen and paper)

100% 230

Now make a new row for 50%

100% 23050%

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

100% 23050% (half of 230) 115

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

100% 23020%

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

100% 23050% (half of 230) 11520%10% (one decimal point less) 23.0

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

100% 23050% (half of 230) 11520% (double of 10%) 4610% (one decimal point less) 23.0

Our master table is ready, now Imagine there is a big water tank with total capacity of196 lit.

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

answer is more than 50% (if % value of 196/230 is asked)1.answer is more than 5 (if absolute value 196/23 is asked)2.

so eliminate answer options that donot meet these criteria.

Move on

Tank Filled Buckets196 115 50%Total 115 50%


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There is still some space left in the tank so lets throw a 20% bucket

Tank Filled Buckets196 115 50%

046 20%Total 161 70%

Or you can add 10% bucket two times, youll get same result.

Its clear that our answer is bigger than 70%. So eliminate any options less than 70%

Hmm, so far weve filled 161, It can still accommodate another 10% bucket


023 10%Total 184 80%

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

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

Master Table Moving decimal numbers100% 23050% (half of 230) 115 5% 11.520% (double of 10%) 232= 46 2% 4.610% (one decimal point less) 23.0 1% 2.3

In the exam, you dont have to actually write new columns of 5%, 2% and 1%, justvisualize them in your head, by shifting the decimal to one point leftwards.

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


011.5 5%Total 195.5 85%

By this time you get the idea that

answer is just a little higher than 85% (if % of 196/230 is asked)1.answer is just a little higher than 8.5 (if absolute value 196/23 is asked)2.

so eliminate any answer options that are not meeting this criteria.

Still if two or more options remain. For example

8.52a.


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8.57b.

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

Well, Total capacity is 196 lit. and so far we filled up 195.5 so, 0.5 lit is still empty. Butno bucket is small enough to carry water in this scale. Solution= create more buckets,by shifting decimal points in the Master Table.

Master Table Moving decimal numbers

100% 230 Phase I Phase II50% (half of 230) 115 5% 11.5 0.5% 1.1520% (double of 10%) 232= 46 2% 4.6 0.2% 0.4610% (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 is clear that 0.2% bucket (0.46 isvery close) so lets use it.

Tank Filled Buckets196 195.50 85%

000.46 0.2%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 more buckets and proceed in the samemanner.

Important sidenotes

Whenever you have to do long-division e.g. 256/29, always make the denominator(bottom number i.e. 29) very close to the top number (256) and take that as100%. That is 290=100%. And then rephrase question: 256 is how much % of290, then proceed according to the method you just learned. Youll get 88.27%.but our question was 256/29. Recall that youve 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 we had added earlier. So instead of100, there remains only 10

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

If there is 7526/67 then? Again same method, 7526 is how much % of 6700?Youll get 112.3%. this time weve added two zeros more (i.e.we used 6700

2.


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instead of 67).

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 remainsonly 1

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

This method looks awkward and tiresome initially, but once youve enoughpractice of doing mental addition then its way easier than the Vedic Mathsconcept of double or triple digit division (because in Vedic method, many a timesyouve to adjust and carry over the numbers= not very convenient).This method can be used for three-digit, four digit divisions also.You can do any division as long as you can find out 10%, 20% and 50% of anumber (and consequently 1%, 2%, 5%, by shifting decimal places.)

Applications of ^this method

Percentage calculation or Long Division has direct or indirect applications in followingtopics:

Profit Loss1.Data Interpretation, especially those based on Pie-charts.2.Compound interest, Simple Interest Rate, Population Growth: by the way, theycan be solved without mugging up formulas, click me to know how!

3.

Mixture-Alligiation, Wine-water, Metal alloys: can be solved without mugging upformulas, click me to know how!

4.

Time-Speed-Distance, Time and Work, Pipes and Cisterns, Boats and Railways.All of them are based on the STD formula: speed x time = distance. So there isalmost always a situation where two variables are given and third is to be found=division. All of them can be solved by mugging only single STD formula.Techniques are scattered around on this page: Mrunal.org/aptitude

5.

Test your skill

Question % Absolute Value Hint: 100% is231/19 190181/29 290158/117 117198/67 67 (because 670 would be too far)67/51 5151/29 29158/117 1178189/541 5410


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URL to article: http://mrunal.org/2012/11/aptitude-long-division-two-digit-division-calculation-without-tears-and-without-boring-vedic-speed-maths.html

Posted By Mrunal On 18/11/2012 @ 00:33 In the category Aptitude


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