Question

If 15% of 40 is greater than 25% of a number by 2, then find the number.

Answer 1

Hint: For solving questions on percentage, one should remember that the sign % is replaced by $ \times \dfrac{1}{{100}}$and ‘of’ is replaced by a simple $ \times $(multiplication) sign.
So, if it is given P% of y = x, then it can be written as:
$
  P \times \dfrac{1}{{100}} \times y = x \\
   \Rightarrow \dfrac{P}{{100}} \times y = x \\
 $
And then you can simplify it.
Use this in the given question to find the percentage of 40 and the unknown number x.

Complete step by step answer:
 Let the number required to find be $x$.
Now, 15% of 40 is greater than 25% of $x$ by 2.
15% of 40 is: $\dfrac{{15}}{{100}} \times 40 = \dfrac{3}{{20}} \times 40 = 3 \times 2 = 6$
25% of x is: $\dfrac{{25}}{{100}} \times x = \dfrac{1}{4} \times x = \dfrac{x}{4}$
So, here it is given that 6 is greater than $\dfrac{x}{4}$ by 2.
This means the difference between them is 2.
$
   \Rightarrow 6 - \dfrac{x}{4} = 2 \\
   \Rightarrow \dfrac{{24 - x}}{4} = 2{\text{ }}\left( {{\text{taking LCM in denominator}}} \right) \\
   \Rightarrow 24 - x = 2 \times 4 \\
   \Rightarrow 24 - x = 8 \\
   \Rightarrow x = 24 - 8 = 16 \\
 $
So, the required number is 16.

Note: Percentage is just a fraction which gives you an idea about how many parts per 100 units of a given thing does something contain or contributes.
For example: If we say a boy gets 25% of a pizza slice from a whole pizza, then it means he got $\dfrac{{25}}{{100}} = \dfrac{1}{4}$ that is 25 parts per 100 or 1 out of the 4 equal slices of the pizza.