Question

The average weight of a class of ${\text{24}}$ students is ${\text{35 Kg}}$. If the weight of the teacher is included the average rises by ${\text{400g}}$. The weight of the teacher is ­­­­­.
$\left( {\text{A}} \right){\text{ 50 Kg}}$
$\left( {\text{B}} \right){\text{ 55 Kg}}$
$\left( {\text{C}} \right){\text{ 45 Kg}}$
$\left( {\text{D}} \right){\text{ 53 Kg}}$

Answer 1

This question is based on average concepts.
Here given that the average weight of a class of ${\text{24}}$ students.
Suppose the weight of the teacher is included, the average rises by ${\text{400g}}$.
Now we want to convert grams into kilograms using the formula and then we find the weight of the teacher.
Finally we get the required answer.

Formula used: ${\text{Average=}}\dfrac{{{\text{sum of these data values}}}}{{{\text{number of data values}}}}$

Complete step-by-step solution:
We know that, average = $\dfrac{\text{sum of all weight of 24 students}}{{number{\text{ }}of{\text{ }}students}}$
Let sum of all weight of ${\text{24}}$ students be denoted by ${\operatorname{w} _1} + {\operatorname{w} _2} + ... + {\operatorname{w} _{24}}$
Therefore average = $\dfrac{{{\operatorname{w} _1} + {\operatorname{w} _2} + ... + {\operatorname{w} _{24}}}}{{24}}$
Given that the average weight of $24$ students is ${\text{35 Kg}}$.
Thus $\dfrac{{{\operatorname{w} _1} + {\operatorname{w} _2} + ... + {\operatorname{w} _{24}}}}{{24}} = {\text{35 Kg}}$
On cross multiplying we get,
$\Rightarrow {\text{ }}{\operatorname{w} _1} + {\operatorname{w} _2} + ... + {\operatorname{w} _{24}} = {{35 \times 24}}$
On multiplying we get,
$\Rightarrow {\text{840}}$
Let the teacher’s weight be ${\operatorname{w} _{25}}$.
Then the number of person = ${\text{24 + 1 = 25}}$
If the weight of the teacher be included the average rises by ${\text{400g}}$.
Then, new average = $\dfrac{{{{\text{w}}_{\text{1}}}{\text{ + }}{{\text{w}}_{\text{2}}}{\text{ + }}...{\text{ + }}{{\text{w}}_{{\text{24}}}}{\text{ + }}{{\text{w}}_{{\text{25}}}}}}{{{\text{25}}}}$= ${\text{35 Kg + 400 g}}$
Now we convert gram in to kilogram
We know that, ${\text{1000 g = 1Kg}}$
$\Rightarrow {\text{ 100 g = 0}}{\text{.1 Kg}}$
Multiply $4$ on both side we get,
$\Rightarrow {\text{ 400 g = 0}}{{.1 \times 4 = 0}}{\text{.4 Kg}}$
Therefore, New average = $\dfrac{{{{\text{w}}_{\text{1}}}{\text{ + }}{{\text{w}}_{\text{2}}}{\text{ + }}...{\text{ + }}{{\text{w}}_{{\text{24}}}}{\text{ + }}{{\text{w}}_{{\text{25}}}}}}{{{\text{25}}}}$= ${\text{35 Kg + 0}}{\text{.4 Kg}}$ = ${\text{35}}{\text{.4 Kg}}$
$\Rightarrow {\text{ }}{{\text{w}}_{\text{1}}}{\text{ + }}{{\text{w}}_{\text{2}}}{\text{ + }}...{\text{ + }}{{\text{w}}_{{\text{24}}}}{\text{ + }}{{\text{w}}_{{\text{25}}}}$= ${\text{35}}{{.4 \times 25 = 885}}$
Now we find out weight of the teacher
That is we find ${\operatorname{w} _{25}}$
$\Rightarrow {\text{ 840 + }}{{\text{w}}_{{\text{25}}}}{\text{ = 885}}$
$\Rightarrow {\text{ }}{{\text{w}}_{{\text{25}}}}{\text{ = 885 - 840 = 45 Kg}}$
Therefore the weight of the teacher is ${\text{45 Kg}}$

Hence the correct option is $\left( {\text{C}} \right)$.

Note: Must be careful to convert gram into kilogram.
A kilogram is one thousand grams.
This means that to get kilogram from grams, you just need to divide the number of grams by $1000$.
Labeling your answer with the proper units is important.
Suppose we get grams form kilogram, you just need to multiply the number of kilograms by $1000$