Marks obtained by students in English $46\% $, Mathematics $67\% $, Sanskrit $72\% $, Economic $58\% $, Political science $53\% $ and History $53\% $. If it is agreed to given double weights to marks in English and Mathematics as compared to other subjects, the weighted mean is
A. $58.43$
B. $48.43$
C. $57.75$
D. None of these

Hint: According to given in the question we have to determine the weighted mean when : Marks obtained by student in English $46\% $, Mathematics $67\% $, Sanskrit $72\% $, Economic $58\% $, Political science $53\% $ and History $53\% $. If it is agreed to give double weights to marks in English and Mathematics as compared to other subjects. So, first of all we have to convert the given percentage marks into decimal and then to find the required mean we have to use the formula to find the mean which is as mentioned below:

Formula used: $ \Rightarrow $Mean$ = \dfrac{{{m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3} + {m_4}{x_4}.........{m_n}{x_n}}}{{{m_1} + {m_2} + {m_3} + {m_4}....................{m_n}}}................(A)$
Now, we have to substitute all the values in the formula (A) as mentioned just above, and as given in the question that if it is agreed to given double weights to marks in English and Mathematics as compared to other subjects so, we have to double the marks for the subjects English and Mathematics to obtain the required mean.

Complete step-by-step solution:
Step 1: First of all we have to convert the given percentage marks into decimal which can be done by dividing the given marks by 100. Hence,
Marks obtained in English:
$ \Rightarrow \dfrac{{46}}{{100}} = 0.46$
Marks obtained in Mathematics:
$ \Rightarrow \dfrac{{67}}{{100}} = 0.62$
Marks obtained in Sanskrit:
$ \Rightarrow \dfrac{{72}}{{100}} = 0.72$
Marks obtained in Economics:
$ \Rightarrow \dfrac{{58}}{{100}} = 0.58$
Marks obtained in Political science:
$ \Rightarrow \dfrac{{53}}{{100}} = 0.53$
Marks obtained in History:
$ \Rightarrow \dfrac{{53}}{{100}} = 0.53$
Step 2: Now, as given in the question, if it is agreed to give double weights to marks in English and Mathematics as compared to other subjects, we have to double the marks for the subjects English and Mathematics to obtain the required mean. Hence,
Marks in English $ = 2(0.46)$ and,
Marks in Mathematics$ = 2(0.67)$
Step 3: Now, to find the required mean we have to use the formula (A) as mentioned in the solution hint. Hence,
Mean$ = \dfrac{{2(0.46) + 2(0.67) + 0.72 + 0.58 + 0.53 + 0.53}}{{2(1) + 2(1) + 1 + 1 + 1}}$
Now, solving the mean as obtained just above,
$ \Rightarrow \dfrac{{2(0.46) + 2(0.67) + 0.72 + 0.58 + 0.53 + 0.53}}{{2(1) + 2(1) + 1 + 1 + 1}} = \dfrac{{0.92 + 1.34 + 0.72 + 0.58 + 0.53 + 0.53}}{7}$
$
   \Rightarrow \dfrac{{0.92 + 1.34 + 0.72 + 0.58 + 0.53 + 0.53}}{7} = \dfrac{{4.62}}{8} \\
   \Rightarrow \dfrac{{4.62}}{8} = 0.5775
 $
Step 4: Now, we have to convert the obtained decimal mean into percentage which can be done by multiplying the obtained mean with 100. Hence,
$ \Rightarrow 0.5775 \times 100 = 57.75\% $
Hence, with the help of the formula (A) as mentioned in the solution hint we have obtained the required mean.

Therefore option (C) is correct.

Note: It is necessary that we have to convert the given percentage marks into decimal which can be done by dividing the given marks by 100.
As mentioned in the question, if it is agreed to give double weights to marks in English and Mathematics as compared to other subjects, we have to double the marks of the both of the subjects to obtain the required mean.