Question

In an examination, there are three papers and a candidate has to get 35% of the total to pass. In one paper he gets 62 out of 150 and in the second 35 out of 150. How much must he get out of 180 in the third paper to just qualify to pass?
A) 65
B) 62.5
C) 72
D) 71

Answer 1

Hint: We will have to find the total marks of three papers from the given information by doing simple arithmetic operations. Then we will find $35\%$ of total marks which are required for the candidate to pass. Once we get the pass percentage we will make use of it to calculate the required number by simple arithmetic operations.

Complete step by step answer:
Candidates got $62$ out of $150$ in one paper & $35$ out of $150.$
Total marks of the examination $=150+ 150+180 =480$
           Percentage required to just qualify the examination: $35\%$
To find: Marks required in third paper to pass the exam
Let marks required in third paper to pass the exam be $x$ out of $180$

So, to find this, we will have to find 35% of total marks = $35\% $ of $480$
                                                                                                   = $\dfrac{{35 \times 480}}{{100}}$
                                                                                                   = $24 \times 7$
                                                                                                   = $168$
So, candidates need to obtain 168 total marks to just qualify the exam.
We know,
Marks obtained in 1st paper + marks obtained in 2nd paper + marks obtained in 3rd paper = 168
$ \Rightarrow $ $62 + 35 + x = 168$
On simplification of the above equation, we get
$ \Rightarrow $ $x = 168 - 62 – 35$
Simplifying further to get the value of $x$,
 $\therefore $ $x = 71$

Therefore, The student needs to get 71 marks out of 180, just to qualify the exam. So, Option D is the correct answer.

Note:
Sum of marks obtained in three papers should be equal to $35\%$ of total marks to just qualify the exam. So, we need to make an equation implying addition of marks obtained equal to the required percentage of total marks & then solve the equation carefully. Ultimately unknown value obtained from solving the linear equation will be the answer.