The average marks per student in a class of $30$ students were $45$. On rechecking it was found that marks had been entered wrongly in two cases. After correction these marks were increased by $24$ and $34$ in the two cases. The correct average marks per student are
$(1) 75 ;\ \ (2) 60 ;\ \ (3) 56 ;\ \ (4) 47.$
On the first look this looked very easy but when done I was left guessing I did not understand the question properly.
The average marks per student in a class of $30$ students were $45$ when the counting was flawed. So total marks in that case was $30\times 45=1350$ . Suppose for student $A$ and $B$ marks had been entered wrongly as $'a'$ and $'b'.$ After rechecking the marks were increased by $24$ and $34$. So , now $A$ has $a+24$ and $B$ has $b+34$. So total marks now is $1350+24+34=1408$. Then the correct average is $1408/30 =46.93$ which is not same as any of the options.
So has there been a mistake in printing or my understanding $?$