Percentages for CLAT 2020
Before diving in the concepts of Percentages, I would like you to familiarize with the reciprocals of numbers from 1 to 30. You might think that you are good at calculations and you can solve questions without these shortcut conversion numbers, but believe me, saving even 10 seconds of calculation in the exam can do wonders for your other sections.
List of reciprocals in terms of percentages:
1/2 = 50%
1/3 = 33.33%
1/4 = 25%
1/5 = 20%
1/6 = 16.66%
1/7 = 14.2857%
1/8 = 12.5%
1/9 = 11.11%
1/10 = 10%
1/11 = 9.09%
1/12 = 8.33%
1/13 = 7.69%
1/14 = 7.1428%
1/15 = 6.67%
1/16 = 6.25%
1/17 = 5.88%
1/18 = 5.55%
1/19 = 5.25%
1/20 = 5%
1/21 = 4.75%
1/22 = 4.54%
Similarly, find the reciprocals of numbers till 30 and remember them.
Some tricks to remember the above reciprocals are:
1/2, 1/4, 1/8, 1/16 so on; if you observe the series closely you will see the pattern of multiple of 2 in the denominator and hence percentages increases as the division of 2 happens with every added 2.
1/9 and 1/11 have each other as there reciprocals.
Reciprocal of 1/7 has 6 digits (142857) which rotate as the numerator changes to multiple of 7. i.e., 2/7 = 28.5714%.
If you add 0.25 in reciprocal of 20 you will get reciprocal of 19 while if you subtract 0.25 from reciprocal of 20 you will get reciprocal of 21.
Note: “Also other than these reciprocals you will need to have the idea about the tables of these reciprocals (2/3, 4/7 etc)”
Percentages: Break the word and you will see it is made of Per+Cent i.e., Cent means 100 thus per cent means part per 100. It is expressed as x% which means x part of a hundred.
Ex: (A) 25% of 100 means 25/100*100= 25 out of 100.
(B) 25 per cent of 164 = (25/100)*164 =41
Suppose you need to find “a” per cent of “b”; this would mean you need to find a/100 of b i.e., (a*b/100).
How to find what per cent of x is y: we have to find what part of x is y, therefore x would be base in such a case. And the formula for the same would be (y/x)*100
Change in Percentage: When we need to check what is the percentage change from the initial value, for that we will take the initial value(x) at the base and new value(y) at the numerator, therefore the formula would be (new value/initial value)*100 or (y/x)*100
Relative percentage concept: When two or more quantities percentage are compared then it is considered as a Relative percentage.
Example: P’s income is 25% more than Q, then what per cent Q’s income is less than P’s income.
Solution: Let Q’s income be 100, 20% of 100 would be 20 (1/5 of 100), therefore P’s income would be 100+25 = 125.
Now we need to find how much Q’s income is less than P, in such a case Remember if one quantity is more than other by x than the same cannot be less than the earlier one by x because the base is different in both the cases.
Here when the comparison is with P then the base will be P and numerator will have the difference in the income of P and Q.
i.e., (25/125)*100 = (1/5) *100 = 20%
Hence, Q’s income would be 20% less than P’s income.
From the above example, we can derive a formula for such cases that would have the difference at numerator and base would be given per cent + 100 i.e., x*100/(100+x)
Increase in percentage: If x is increased by y per cent than, first find y per cent of x then add that to x.
y per cent of x is (y*x)/100,
increased value = x+(x*y)/100
= x(1+ y/100)
Decrease in percentage: If x is decreased by y per cent than, first find y per cent of x then subtract that from x.
y per cent of x is (y*x)/100,
decreased value = x-(x*y)/100
Price and Quantity adjustment: If price or quantity increase/decrease by x% then per cent increment/deduction to bring it back to the original point is x*100/(100+x)
Successive Percentage change: When there is successive percentage increment of any quantity by a% and b% then we use the formula (a+b+(a*b/100))%