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Fast Calculation Techniques for BANK/SSC Exams: (Part 1)

By Calculations, we do not mean integral calculations just like multiplying 2 digit numbers quickly or find the cube of 26 or square roots.

We mean approximate calculations such as dividing 557 by 852 and finding that value as a percentage or looking at a line graph and comparing (not calculating) fractions to find the year with highest possible increase. Let us took at some possible approaches for these kinds of calculations.

557/852

557/852: One possible way of handling this to approximate. Since we have to divide, you will always approximate the denominator. Hence you could take your 852 to 900. Hmm, you must be wondering was that a typo? NO. If you had to guess as a ballpark what 557/852 will look like then I am sure we can see that this will be close to 2/3. So, if you are adding 48 to the denominator then to conserve the value of the fraction the value of the fraction you must add 32 i.e. 2/3 of 48 to the numerator. So your original fraction of 557/852 is approximated to 589/900. Hence, the value of the fraction 557/852 = 589/900=0.654 or 65.4% .Exact value of 557/852 is 65.37%, so our answer is quite close to the actual answer.

Let’s understand this further by doing one more example. Suppose you had to find 1326/769. I could approximate 769 to 800 or to 750. 750 is not so bad because it is ¾ of a thousand. Let’s start with 800. If we assume 769 to 800 we need to add 31 to the denominator. Approximately the fraction looks like less than 2 let’s say around 1.8 then for 31 to the denominator we need to add a value a little less than 31×2=62 let’s say 55.So 1326/769 = (1326+55)/(769+31) = 1381/800 = 1.724 ; again our approximate answer is a very good approximation.

What if we had worked with 750? Let’s see; To get 750 we need to subtract 19 from the denominator which means that to conserve the original value of the numerator we need to subtract a little less that 2×19=38 let’s say 35. So 1326/769= (1326-35)/769-19 = 1291/750 = 1291 x 4/3000 = 1.721. As we already know that the exact value 1.724, At the risk of repeating myself let me mention again that our approximate answer is a very good approximation.

Let’s just put all this in nice simple bullet points: (where would we be without bullet points?)

  • Always approximate the denominator.
  • Approximate close to the number. So 769 become 800 but do not become 1000. The farther you take your denominator the less exact your answer.
  • You take a ball park of the fraction: it cannot be a very fine tuned approximation: if you are doing a fine tune you might as well divide exactly instead of approximating.
  • Whatever you do to the denominator you do the same thing but proportionately to the numerator.

We also have another method in which we visualize 10%, 1% .1% of denominator and then fit it to the denominator.  Let’s take few examples

1132/1069 =1132/1069 = 1 + 63/1069

Now, 10% of 1069 = 107 (approx.) so, 63 = almost 6% and, 6% = .06.

Therefore, Ans. 1.06

41/695 =? %                        10% of 695 = 69.5   so, 5% will be –   35 (approx.)

We need 6 more to reach 41. . . . .

1% of 695 will be close to 7, so 0.9% will be almost 6 so, the Ans. is 5% + 0.9% = 5.9%

12.71/29.5 =? %                12.71/29.5   => 1271/2950 => 1270/ 2950 => 127/295

10% of 295 = 29.5,            Hence, 20% = 59 and therefore 40% =118

We are still short of -> (127- 118) = 9

Now, what is 9 as a %age of 295?              1% = 3 (almost), so 9 => 3%         so, Ans.  (40% + 3 %) = 43%

400/2078 =? % 400/2078 => 400/2080 => 40/208 Now, 20% of 208 = 41.6, we have overshot by 1.6,

What % of 208 is 1.6?      Clearly 1% of 208 is 2 and therefore 1.6 = .8%

So, the Ans. is (20% -0.8%) => 19.25%

5/1007.5 =?%                                     10% of 1007.5 = 100.75

That leaves a gap of 6.75               Now, 1% of 1007.5 = 10 ;

So 6.75 is almost 0.67 %.                Hence, my ans. is 10.65.

3/186 = ?%                                          10% of 186 = 18.6

Therefore 20%= 37.2 and 40%=74.4 ( 4 more to go )

2% will be 3.7                                     Therefore, my Ans. will be 42% ( closest )

Fast Calculation Techniques for SSC/BANK Exams: PART -2

RECIPROCAL EQUILENT OF %

Off course you can easily calculate 25% of 640 as it is 1/4th of 640, or you can easily do 40 % of 360 as it is 2/5 of 360 i.e. 144.

But what about 52.6 % 3800?

Or what about 27.27 % of 65527?

To do this kind of first you should be very comfortable with the fraction equivalent of percentages. Let’s learn them till 1/30.

1 100% 1/11 9.09% 1/21 4.76%
1/2 50% 1/12 8.33% 1/22 4.54%
1/3 33.33% 1/13 7.69% 1/23 4.35%
1/4 25% 1/14 7.14% 1/24 4.16%
1/5 20% 1/15 6.66% 1/25 4%
1/6 16.66% 1/16 6.25% 1/26 3.84%
1/7 14.28% 1/17 5.88% 1/27 3.7%
1/8 12.5% 1/18 5.55% 1/28 3.57%
1/9 11.11% 1/19 5.26% 1/29 3.45%
1/10 10% 1/20 5% 1/30 3.33%

How to remember reciprocals?

1/9=11.11% ; 2/9= 22.22%; 4/9 = 44.44%; 5/9 = 55.55%, 7/9= 77.77%.

1/11=9.09%; 2/11= 18.18% ; 3/11 = 27.27% ; 7/11= 63.63%

1/8=12.5% » 3/8= 37.5% » 5/8= 62.5% » 7/8= 87.5%

Calculating percentages

32.5% of 720 =?                 32.5% = 20% + 12.5%= (1/5   + 1/8) of 720

=144 + 90=234

We could have also done the following splits

3 x 10% + 2.5%   or 25% + 5% + 2.5% or approx. 33.33%

Now let’s calculate these.

09 % of 220= (50% + 9.09%) of 220 = 110 + 1/11 of 220 = 110+ 20 =130.

6 % of 480 = (10/24) x 480 = 200.

5 % of 720 = (62.5% + 5%) of 720 = 5/8 x 720 + 36 = 450 +36 = 486.

33% of 666 = 10/12 of 666 = 5/6 of 666 = 555

44 % of 981.36 = 4/9 of 981.36 = 436.16

72% of 6402 = 8/11 of 6402 = 4656

75% 6666 = 66.66% of 4575 (a% of b is equal to b% of a) = 2/3 of 4575 = 3050.

14% of 280 = (40% + 7.14%) of 280= 2/5 x 280 + 1/7 x 280 = 112 + 40 = 152.

6 % of 3800 = 10/19 of 3800 = 2000

200/5.88 = 2×17 = 34. (As 5.88= 100/17)

Practice question for you.

5 % of 80                              09 % of 65527                                     6 % of 57.14                                        55% 19.8

35 % 230                               63 % of 546172                                  27 % of 5555                                       88 % of 99999

476 % of 420                       6 % of 1400                                         345 % of 58000                                  45.45% of 7272

416% of 24000                   25 % of 720                                         7 % of 54                                              56 % of 666