Solve Percentage Problems Easily: Quick Tricks & Methods

In placement exams, speed is just as important as accuracy. While understanding concepts is crucial, knowing how to solve problems quickly can give you a competitive edge. Percentages are a common topic in aptitude tests, and mastering them can save you valuable time. In this guide, we’ll explore powerful shortcuts, mental math techniques, and practical examples to help you solve percentage problems faster and more efficiently.

Why Speed Matters in Placement Exams

Placement exams often have tight time constraints, and solving problems quickly can make the difference between success and failure. By learning shortcuts and practicing regularly, you can improve your problem-solving speed and accuracy. Let’s dive into some key techniques to master percentages.

The Golden Rule: a% of b = b% of a

Did you know that a% of b is the same as b% of a? Let’s break it down:a%×b=a100×b=a×b100a%×b=100a×b=100a×bb%×a=b100×a=b×a100b%×a=100b×a=100b×a

From this, we can see:a%×b=b%×aa%×b=b%×a

This simple trick can save you a lot of time in calculations.

Example:

Find 32% of 50.

Instead of calculating 32% of 50 directly, use the rule:32%×50=50%×3232%×50=50%×32

Since 50% of a number is half of it:50%×32=322=1650%×32=232=16

Thus, 32% of 50 = 16.

Advanced Applications of the Rule

Example:

Find 45% of 280 + 28% of 450.

Using the rule a% of b = b% of a, rewrite 28% of 450 as 45% of 280:28%×450=45%×28028%×450=45%×280

Now, the expression becomes:45%×280+45%×280=90%×28045%×280+45%×280=90%×28090%×280=(100%×280)−(10%×280)=280−28=25290%×280=(100%×280)−(10%×280)=280−28=252

By recognizing this pattern, you can solve the problem in seconds!

Mental Math Techniques for Percentages

Example:

Find 42% of 250 + 12.5% of 840.

Using the rule, rewrite 12.5% of 840 as 25% of 420:12.5%×840=25%×42012.5%×840=25%×420

Now, simplify the expression using mental math:

42% of 250 = (40% + 2%) of 250 = (100 + 5) = 105
25% of 420 = 14×42041×420 = 105

Adding both, we get:105+105=210105+105=210

Solved Examples

Q1: A batsman scored 110 runs, including 3 boundaries (4 runs each) and 8 sixes (6 runs each). What percentage of his total runs did he score by running between the wickets?

Solution:

Runs scored without running:(3×4)+(8×6)=12+48=60

Runs by running:110−60=50110−60=50

Required percentage:(50110)×100=45511%(11050)×100=45115%

Q2: In an election, a candidate received 55% of the valid votes, while 20% of the total votes were invalid. If the total votes were 7500, how many valid votes did the other candidate get?

Solution:

Valid votes:80%×7500=600080%×7500=6000

Votes received by the other candidate:45%×6000=270045%×6000=2700

Thus, the other candidate received 2700 valid votes.

Quick Formula Recap

Final Quantity After Replacements:Q×(1−P100)nQ×(1−100P)n
Increase/Decrease in Population or Growth Rate:P=(NewValue−OldValue)OldValue×100P=OldValue(NewValue−OldValue)×100
Error Percentage Calculation:CorrectValue−IncorrectValueCorrectValue×100CorrectValueCorrectValue−IncorrectValue×100
Election Vote Calculation:ValidVotes=(TotalVotes−InvalidVotes)ValidVotes=(TotalVotes−InvalidVotes)

Conclusion

Always apply a% of b = b% of a to simplify calculations.
Convert percentages into fractions for quick mental math.
Practice regularly to build speed and accuracy.

By mastering these techniques, you can solve percentage problems faster and more accurately, giving you an edge in placement exams.