In a certain examination, a candidate answered $25$ questions and two-fifth of the rest of the total number of questions, and he found that he has answered only $60\%$ of the total number of questions. How many questions did he answer?

Let the total number of questions be $x$.
The number of remaining questions after answering $25$ questions is $x-25$.

According to the question, the total number of questions answered is:

$$25+\frac{2}{5}(x-25)=60\%\text{ of }x$$

$$25+\frac{2}{5}x-10=\frac{3}{5}x$$

$$15=\frac{3}{5}x-\frac{2}{5}x$$

$$15=\frac{1}{5}x$$

$$x=75$$

The total number of questions is $75$.
The number of questions he answered is $60\%$ of $75$:

$$\text{Questions Answered}=\frac{60}{100}\times 75=45$$