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Faster calculation methods applied on ‘Real Exam Questions’ – Part II

Let us consider a very simple question that appeared in one of the competitive exams to understand the ‘percentage’ concept- this will help you calculate much faster in a lot of other topics. You would get application-based questions on ‘%’ that might pertain to Simple/Compound Interest, Ratio & Proportion, Profit & Loss, Partnership problems, Time-Speed-Distance or the Data Interpretation (Tables/Charts/Graphs) section. So it is a very important & useful concept! Here is the problem.

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The usual way to solve this problem is to assume a variable ‘x’ as the unknown (?) as shown below:

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Now let us approach the problem in a different way. The first step is to understand 14% as to be ‘made’ up of 1 unit of 10% and 4 units of 1%. Now to calculate 14% of 80, first find 10% and 1% values:

10% of 80 = 8 ;   1% of 80 = 0.8 =>  4% of 80 = 3.2

14% -> 8 + 3.2 = 11. 2

Diagramatically,

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Now we see that we have reached 11.2 and we need 20.7 more to reach the figure ‘31.9‘. So, the next target should be to find out ‘what‘ percentage of 90 is 20.7!

We again start thinking in terms of 10%-1% method; 10% of 90 is 9, so surely the answer option must be greater than 20% (as 2 units of 10% will add 18 and thus we can out rightly reject out options 1 and 3). Now with 20% we have reached a figure ’18’ and we need 2.7 more.  Since 1% gives me ‘0.9’; 3 units of 1% gives me ‘2.7’. Hence answer options should be 23% ( 2 units of 10% and 3 units of 9%) !

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Let use this same concept in one more kind of problem that will help in calculating faster in Data Interpretation section:

A school has a playground where students are participating in National Atheletics Meet 2013. The students belong to one of the three schools- K.V., J.N.V and D.A.V. If number of students of these schools are respectively 295, 432 and 700, what approximate percentage of the total participating students belong to K.V. ?

a.  23.5 %

b.  22.6 %

c.  18.9 %

d. 19.3 %

e. 20.6 %

After reading it once, you would have figured out that the calculation needs to be bit precise as the options are closer. Let us use our 10%, 1% method to check if we could use it here!

First step is to get the total number of students: Add 700 and 300 (Do not add 295; instead add 300 and later minus 5 from the total) and add 432; minus 5 to get the total: 1427. Now, the ratio, that we are looking at, is:

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Find out the 10% and 1% of the denominator. 10% of 1427 is 142.7. To reach 295 we need 2 units of 10% which will result in 285 approx ( 2 times 142.7).  Now 1% of 1427 is 14.27. Since we need only 10 more to reach 295, we can’t add even a single unit of 1% (which is 14.27).

So our answer option should definitely be between 20% and 21% – option e.

If you approach a ‘%’ problem as shown above, you will learn to calculate mentally faster, save time and mark correctly even if the options are closer! Let me know if you have any doubts.

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