Question

sushma , sanidhya and smita are studying in one class . in a class test smita got 20 out 0f 25 and sushma got 16. average marks of all 3 are 19 . how many did sanidhya score​

Answer 1

Given :-

Total marks for which the test was being conducted = 25

Marks scored by Smita in the class test = 20

Marks scored by Sushma in the class test = 16

Let the marks scored by Sanidhya be x .

The average of their scores = 19

$\color{olive} average = \color{hotpink} \frac{sum \: of \: all \: values}{count \: of \: values}$

Which means :-

$= \frac{\texttt{20 + 16 + \: x }}{\texttt{3}} = \texttt{19}$

$= \frac{36 + x}{\texttt{3}} =\texttt{ 19}$

$=\texttt{ 36} + x = \texttt{19 × 3}$

$=\texttt{ 36} \: + \: x \texttt{ \: = 57}$

$= x = \texttt{57 - 36}$

$\hookrightarrow\color{hotpink} x = \: \texttt{21}$

Let us check whether or not we have found out the correct value of x, by placing 21 in the place of x :-

$= \frac{\texttt{20 + 16 + 21}}{\texttt{3}} = \texttt{19}$

$= \frac{\texttt{57}}{\texttt{3}} = \texttt{19}$

$= \texttt{19 = 19}$

$</strong><strong>\hookrightarrow</strong><strong>\texttt{\color{olive}LHS =\color{hotpink} RHS }$

As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct value of x.

Therefore, Sanidhya scored 21 marks in the test .