Question

A student has secured $40\%$ marks to pass. He got 40 marks and failed by 40 marks. The Maximum number of marks is
A). 200
B). 160
C). 180
D). 320

Answer 1

Hint: In this question it is given that a student has secured $40\%$ marks to pass. He got $40$ marks and failed by $40$ marks. Then we have to find the maximum mark. So to find the solution we need to equate the $40\%$ of total mark with the passing mark of the exam.

Complete step-by-step solution:
Let us consider the maximum mark is $x$.
Here it is given that the passing mark is $40\%$.
i.e Passing marks = 40$\%$ of $x$
                              = $$\dfrac{40}{100} \times x$$
                              = $$\dfrac{2}{5} \times x$$
                              = $$\dfrac{2x}{5}$$
Also he got 40 marks in the exam and failed the exam by $40$ marks.
Therefore the passing mark will be $(40+40)$ = $80$ marks
Now according to the question we can write,
$$\dfrac{2x}{5} =80$$
$$\Rightarrow \dfrac{2x}{5} \times 5=80\times 5$$ [multiplying both side by 5]
$$\Rightarrow 2x=400$$
$$\Rightarrow \dfrac{2x}{2} =\dfrac{400}{2}$$ [dividing both side by 2]
$$\Rightarrow x=200$$
Therefore maximum marks is 200.
Hence the correct option is option A.

Note: While solving this type of question you need to know that, (r % of A) can be written as,
r $\%$ of A = $$\dfrac{r}{100} \times A$$
Where, we have transformed the statement into mathematical expression, we replaced $‘\%’$ by $$\dfrac{1}{100}$$ and ‘of’ by $$\times$$.