How to solve Percentage Problems With Ease

How to solve Percentage Problems With Ease

Merely knowing all the concepts is not going to help you ace the placement examinations. There is also a need to solve the questions quickly. You could achieve this through some tricks and a lot of practice. Let’s see how to do this with problems with percentages.



how_to_solve_percentage_problems_with_ease_


Is a% of b the same as b% of a? Stop! Think! Proceed!

Let us verify the above statement.

a% of b = a/100 * b= a*b/100—————– (1)

&

b% of a = b/100 * a= b*a/100——————-(2)

From Equations 1 and 2, it is clear that a% of b has exactly the same value as b% of a.

The above statement reduces our calculation effort in many percentage problems.


Let us take an example.

Calculate 32% of 50. Think about what we discussed! (we know that a% of b and b% of a are the same)

 So, 32% of 50 = 50% of 32.

 Now there is nothing left to calculate,

50% = 1/2

So, 50% of 32= 1/2*32= 16.


If you are good at converting percentages into fractions and know that a% of b is the same as b% of a, you can easily reduce calculation in many percentage problems.

 

Summary: Always try to use the relation a% of b= b% of a. Through practice, you can master this idea and your brain will automatically convert it whenever faced with a similar problem.

 

Let us try another problem. Find the value of 45% of 280 + 28% of 450?

Anybody can solve the above expression, but our purpose is to solve it quickly.

Look at the second term,

28% of 450 can be written as 45% of 280. (if you doubt this you can solve and check for yourself)

Now, our expression becomes,

45% of 280 + 45% of 280= 90% of 280

= (100% of 280) – (10% of 280)

= 280-28

= 252


Alright, next Question:

42% of 250 + 12.5% of 840.


Solution: 

In this question, it does not look directly that here we can apply a% of b = b% of a.

Let’s look at the second expression which is a little complex

12.5% of 840 = 25% of 420 (as 25% of 100 is same as 50% of 50) Now our expression becomes.

 


percentage-problem

Now it’s your turn to solve such questions mentally without using a pen. Use pen and paper only for problems you are unable to solve mentally.


Solved Examples

Q.1. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What per cent of his total score did he make by running between the wickets?

Solution: Number of runs made by running = 110 – (3 x 4 + 8 x 6)

= 110 – (60)

= 50.

 Required percentage =(50/110) x 100% = 45 5/11%


Q.2. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. The marks obtained by them are?

Solution: Let their marks be (x + 9) and x.

Then, x + 9 =56(x + 9 + x)100 25(x + 9) = 14(2x + 9)

 3x = 99

 x = 33

So, their marks are 42 and 33.



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Q. 3. What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?

Solution: Clearly, the numbers which have 1 or 9 in the unit’s digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such numbers =14

 Required percentage =14/17 x 100% = 20%


Q.4.If 20% of a = b, then b% of 20 is the same as:

  1. 4% of a
  2. 5% of a
  3. 20% of a
  4. None of these


Solution: Option A

20% of a = b      20/100 *a = b 

b% of 20 = (b/100 * 20) =(20/100 * 1/100 * 20)=4/100a = 4% of a.


Q.5.In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is  the number of students of 8 years of age which is 48. What is the total number of students in the school?


Solution: Let the number of students be x. Then,

Number of students above 8 years of age = (100 – 20)% of x = 80% of x.

 80% of x = 48 +2of 48380x = 80100 x = 100.


Q.6. A student multiplied a number by 3 instead of 5 What is the percentage error in the calculation?


Solution:

Let the number be x.

Then, error =5x/3 -3x/5 =16x/5.

Error% =(16x/5 * 3/5x * 100)% = 64%.



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Q.7.In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:


Solution: Number of valid votes = 80% of 7500 = 6000.

 Valid votes polled by other candidate = 45% of 6000 =45/100 * 6000 = 2700


Q.8.Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 per cent of the sum paid to Y, how much is Y paid per week?


Solution: Let the sum paid to Y per week be Rs. z.

Then, z + 120% of z = 550.

 z +120/100 * z = 550

11/5z = 550

z= 550 * 5/11


Q.9.The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percentage increase in population per year is?


Solution: Increase in 10 years = (262500 – 175000) = 87500.

Increase %= (87500/175000 * 100)=50%

Required Average = (50/10)% = 5%




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