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

In Aptitude by Support Staff

Ok this isn’t about boring vedic maths technique so don’t run away, yet!
  • One of  the biggest problem with IBPS/Bank, SSC, CAT, CMAT type of exams= you’ll encounter long division and percentage (%) calculation every now and then, directly or indirectly (in Data interpretation questions).
  • And If you’re not good with speed maths, you’ll waste a lot of time in such stupid calculations.

For the the aptitude questions of  Bank/MBA exams, Knowing the answer approach is not sufficient. You also need to get the answer quickly and accurately. Otherwise someone else will tick more answers and he’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=?
  1. 49.3%
  2. 60.1%
  3. 85.2%
  4. 85.7%
  1. 4.93
  2. 6.01
  3. 8.52
  4. 8.57
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 is actually in ‘doing’ that calculation or division (196/23). Here I’ll show a single method, to solve both type of calculations. As long as you know how to add two numbers, and how to multiply a number with 5, you can execute this method effortlessly.

First create a “Master Table” (don’t just read it, do this simultaneously using your own pen and paper)

100% 230

Now make a new row for 50%

100% 230
  • So either divide 230 by 2=115
  • or 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% 230
50% (half of 230) 115

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

100% 230

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

100% 230
50% (half of 230) 115
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. That’s our 20%. Fill up the table.

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 big water tank with total capacity of 196 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 space will be left.
By this time you get the idea that

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

so eliminate answer options that donot meet these criteria.

Move on

Tank Filled Buckets
196 115 50%
Total 115 50%

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

Tank Filled Buckets
196 115 50%
046 20%
Total 161 70%

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

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

Hmm, so far we’ve filled 161, It can still accommodate another 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!

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

 Master Table Moving decimal numbers
100% 230
50% (half of 230) 115 5% 11.5
20% (double of 10%) 23×2= 46 2% 4.6
10% (one decimal point less) 23.0 1% 2.3

In the exam, you don’t have to actually write new columns of 5%, 2% and 1%, just visualize them in your head, 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

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

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

Still if two or more options remain. For example

  1. 8.52
  2. 8.57

^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. But no 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 II
50% (half of 230) 115 5% 11.5 0.5% 1.15
20% (double of 10%) 23×2= 46 2% 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 is clear that 0.2% bucket (0.46 is very close) so let’s use it.

Tank Filled Buckets
196 195.50 85%
000.46 0.2%
Total 195.96 85.2%

So the final answer is

  • 196/23=8.52
  • 196/230=85.2%

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

Important sidenotes

  1. 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 as 100%. That is 290=100%. And then rephrase question: “256 is how much % of 290”, then proceed according to the method you just learned. You’ll get 88.27%. but our question was 256/29. Recall that you’ve added one zero more. (290)

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 of 100, there remains only 10

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

  1. If there is 7526/67 then? Again same method, 7526 is how much % of 6700? You’ll get 112.3%. this time we’ve added two zeros more (i.e.we used 6700 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 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 mental addition then it’s way easier than the Vedic Maths’ concept of double or triple digit division (because in Vedic method, many a times you’ve 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 a number (and consequently 1%, 2%, 5%, by shifting decimal places.)

Applications of ^this method

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

  1. Profit Loss
  2. Data Interpretation, especially those based on Pie-charts.
  3. Compound interest, Simple Interest Rate, Population Growth: by the way, they can be solved without mugging up formulas, click me to know how!
  4. Mixture-Alligiation, Wine-water, Metal alloys: can be solved without mugging up formulas, click me to know how!
  5. 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 is almost 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

Test your skill

Question % Absolute Value Hint: 100% is
231/19 190
181/29 290
158/117 117
198/67 67 (because 670 would be too far)
67/51 51
51/29 29
158/117 117
8189/541 5410