Table of contents 
Important Formulas 
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12. Percentage – Ratio Equivalence
Table: Fractions and their percentage equivalents:
 r% change can be nullified by (100r/100 + r)% change in another direction.
Example: An increase of 25% in prices can be nullified by a reduction of [100 x 25/(100 + 25)] = 20% reduction in consumption. If a number ‘x’ is successively changed by a%, b%, c%...
⇒ Final value = The net change after two successive changes of a% and b% is:
Example: What is 27% of 90?
Solution: Our thought process mostly would be 10% of 90 is 9, 5% is 4.5 and 2% is 1.8
hence 27 % of 90 = 18 + 4.5 + 1.8 = 24.3 (5 seconds max).
There would be faster methods but we are not going to any math Olympiad. Practice this method religiously and you will be quick enough for CAT and similar exams.
Example: What is 90% of 27?
Solution: No need to calculate again, we already did it and got the answer as 24.3!
27% of 90 = 27 x 90 / 100 = 90 x 27 / 100 = 90% of 27
That means when we solve one percentage sum we are actually solving two. And this comes very handy if one problem is much easier to solve than the other one.
Example: What would be the final value if 60 is increased by 30%?
Solution: Final value = 60 x (1 + 30/100) = 78
(Else we know 10% of 60 = 6, so 30% increase should add 18 yielding 78 )
Now what would be the final value if 60 is increased by 30% and then by 50%
Final Value = 60 x (1 + 30/100) (1 + 50/100) = 117
Let the successive increase in percentages be a% and b%. In that case, the total increase will be (a + b + ab/100) % (for decrease use a negative sign).
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