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.
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.
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.
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.
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:
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 483
80x = 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%.
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%