A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination?

The correct option is 150.

To find the maximum marks in the examination, let us break the problem down into simple logical steps.

Step 1: Understand the passing criteria
A student needs to secure 40% of the total maximum marks to pass the examination.

Step 2: Determine the passing marks
We are given that the student scored 30 marks and failed by 30 marks. This implies that the student fell short of the passing mark by exactly 30 marks. Therefore, if we add these 30 marks to his score, we will get the minimum marks required to pass.

$\text{Passing Marks}=30+30=60$

Thus, the minimum marks required to pass the examination is 60.

Step 3: Calculate the maximum marks
Let the maximum marks of the examination be represented by $x$.

Since the passing marks are 40% of the maximum marks, we can set up the following relation:

$40\%\text{of}x=60$

We can write this percentage as a fraction to solve for $x$:

$\frac{40}{100}\times x=60$

Simplifying the fraction:

$0.4\times x=60$

To isolate $x$, divide both sides of the equation by 0.4:

$x=\frac{60}{0.4}$

Evaluating the division:

$x=150$

Therefore, the maximum marks in the examination are 150.