Question

In an examination, there are three papers each of $100$ marks. A candidate obtained $53$ marks in the first and $75$ marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of $70$ percent marks?​

Answer 1

Finding the marks in third paper to get an overall of $70$ percent.
$\text{Total marks}=3\times 100=300$ $[\because \text{There are}3\text{papers of}100\text{marks each}]$

$\text{Marks obtained in first paper}=M_1=53$
$\text{Marks obtained in second paper}=M_2=75$
Let $x$ be marks scored in third paper so that he gets
$70\%$.
Hence, $\text{total score}=53+75+x$
$\text{The percentage of marks}=70\%$
$\therefore \frac{53+75+x}{300\times 100}=70$
$\Rightarrow (53+75+x)=70\times \frac{300}{100}$
$\Rightarrow x+128=210$
$\Rightarrow x=210-128=82$
Hence, he should score $82$ marks in third paper to score $70\%$.