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 $\times {\displaystyle \frac{1}{100}}$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:
$$\begin{gathered} P\times {\displaystyle \frac{1}{100}}\times y=x \\ \Rightarrow {\displaystyle \frac{P}{100}}\times y=x \end{gathered}$$
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: ${\displaystyle \frac{15}{100}}\times 40={\displaystyle \frac{3}{20}}\times 40=3\times 2=6$
25% of x is: ${\displaystyle \frac{25}{100}}\times x={\displaystyle \frac{1}{4}}\times x={\displaystyle \frac{x}{4}}$
So, here it is given that 6 is greater than ${\displaystyle \frac{x}{4}}$ by 2.
This means the difference between them is 2.
$$\begin{gathered} \Rightarrow 6-{\displaystyle \frac{x}{4}}=2 \\ \Rightarrow {\displaystyle \frac{24-x}{4}}=2\left(\text{taking LCM in denominator}\right) \\ \Rightarrow 24-x=2\times 4 \\ \Rightarrow 24-x=8 \\ \Rightarrow x=24-8=16 \end{gathered}$$
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 ${\displaystyle \frac{25}{100}}={\displaystyle \frac{1}{4}}$ that is 25 parts per 100 or 1 out of the 4 equal slices of the pizza.