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Hint: We will be using the concept of percentage to tackle this question. We will assume the maximum number of marks to be x. Student got 135 marks and he failed by 15 marks so the total mass required to pass is 150 which means 30% of the maximum marks is equal to 150.

__Complete step-by-step answer:__

Let the maximum number of marks be x.

Also if we have to turn a percentage into a fraction we will just divide by 100.

Here it is mentioned in the question that the student got 135 marks and he failed by 15 marks. Using this information, we get,

Marks achieved by the student \[=135......(1)\]

Marks by which the student failed \[=15......(2)\]

So adding equation (1) and equation (2) we get the total marks needed to pass.

Marks required to pass \[=135+15=150......(3)\]

It is also mentioned in the question that the student has to secure 30% marks to pass, so using this information we get,

\[\Rightarrow 30%\,\text{of }x\text{=150}.........\text{(4)}\]

Now changing the percentage into fraction in equation (4) we get,

\[\Rightarrow \dfrac{30}{100}\,\times \text{ }x\text{=150}.........\text{(5)}\]

Solving for x in equation (5) we get,

\[\Rightarrow x\text{=}\dfrac{150\times 100}{30}=500\]

Hence 500 is the maximum marks.

Note: Whatever the question is asking us to find we will take it to be x, this way it consumes less time. We just have to remember the percentage formula and then read the question properly. In a hurry, we can make a mistake by taking 30% of the total marks required to pass that is 150.

Let the maximum number of marks be x.

Also if we have to turn a percentage into a fraction we will just divide by 100.

Here it is mentioned in the question that the student got 135 marks and he failed by 15 marks. Using this information, we get,

Marks achieved by the student \[=135......(1)\]

Marks by which the student failed \[=15......(2)\]

So adding equation (1) and equation (2) we get the total marks needed to pass.

Marks required to pass \[=135+15=150......(3)\]

It is also mentioned in the question that the student has to secure 30% marks to pass, so using this information we get,

\[\Rightarrow 30%\,\text{of }x\text{=150}.........\text{(4)}\]

Now changing the percentage into fraction in equation (4) we get,

\[\Rightarrow \dfrac{30}{100}\,\times \text{ }x\text{=150}.........\text{(5)}\]

Solving for x in equation (5) we get,

\[\Rightarrow x\text{=}\dfrac{150\times 100}{30}=500\]

Hence 500 is the maximum marks.

Note: Whatever the question is asking us to find we will take it to be x, this way it consumes less time. We just have to remember the percentage formula and then read the question properly. In a hurry, we can make a mistake by taking 30% of the total marks required to pass that is 150.

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