Question

In an examination, a student needs to get $45\%$ to secure passing marks. A student got 138 marks and failed by $15\%$. What were the maximum marks?
(a)400
(b)450
(c)460
(d)500

Answer 1

Hint: First of all, we will find the maximum percentage of marks a student can get in an exam by taking the difference of marks he needs to get and the marks by which he failed. Then using that we will find the maximum marks by equating it with 138 marks the student got and we will get our answer.

Complete step-by-step answer:
Now, in question it is given that a student needs to get $45\%$ to secure passing marks and he failed by $15\%$, from this we can say that student got $45\%$ of the maximum marks and he failed by $15\%$ of the maximum marks.
Now, taking the difference of maximum marks a student needed and the marks by which the student failed, we will get the maximum marks he can get.
Now, we will suppose the maximum marks student can get as $x$, then we will get the equation as,
$\dfrac{45}{100}\times x-\dfrac{15}{100}\times x=\dfrac{30}{100}\times x$.
Now, above we have got the marks the student got and in question we are given that 138 are the marks the student got, so on equating them we will get,
$0.3\times x=138$
$\Rightarrow x=\dfrac{138}{\dfrac{30}{100}}$
$\Rightarrow x=\dfrac{138\times 100}{30}=460$
Hence, we can say that the maximum marks were 460.
Thus, option (c) is correct.

Note: In such a question, students might get confused between maximum and minimum marks and due to that they might make mistakes in solving the sum. They also might not understand the difference of maximum marks needed and the marks by which students failed and due to that they won’t be able to solve the question and might not get the answer.