Question

In a class of $250$ students, $75.8\% $ took French and $49.4\% $ took Latin. How many students took French and Latin ?
A)$189.0$
B)$123.0$
C)$63.0$
D)$90.0$

Answer 1

Hint: Calculate the number of students who took French and the number of students who took Latin. Take the sum, the number of students who took both French and Latin is the number by which the sum exceeds the total number of students, i.e., $250$

Complete step-by-step answer: Number of students who took French
$ = 75.8\% $of $250$
$
   = \dfrac{{75.8}}{{100}} \times 250 \\
   = 189.5 \\
 $
Number of students who took Latin
$ = 49.4\% $ of $250$
$
   = \dfrac{{49.4}}{{100}} \times 250 \\
   = 123.5 \\
 $
Since, ($189.5 + 123.5 = 313$) which is more than $250$, there must be some kind of overlap, that is, it is not possible that the two groups are mutually exclusive.
Total number of students is $250$
The overlap conveys the students who took both French and Latin.
Hence, the number of students who took both French and Latin are :
$
  313 - 250 \\
   = 63 \\
 $
Therefore, C) is the correct answer.

Note: This can be solved in one more way, that is, by letting the total number of students be $100$, then the number of students who took French becomes $75.8$ and who took Latin becomes $49.4$. Using the same explanation, the number of students who took both subjects becomes ($75.8 + 49.4 - 100 = 25.2$). Note that this will give a percentage of students. To calculate the actual number, use $25.2\% $ of $250$which is equal to $63$.