## 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 with through some tricks and a lot of practice. Let’s see how to do this with problems on percentages.

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

Let us verify above statement.

a% of b = a/100 * b= a*b/100----------------- (1)

&

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

From equation 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 what we discussed! *(we know that a% of b and b% of a are 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 in converting percentage into fraction and you know that a% of b is same as b% of a, then 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 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.