Question

14. The mean weight of a class of 34 students is 46.5 kg. if the weight of
the teacher is included the mean rises by 500g. Find the weight of the
teacher​

Answer 1

Given :

• The mean weight of a class of 34 students = 46.5 kg
• If the weight of the teacher is included the mean rises = 500 g

To find :

• The weight of teacher

According to the question,

➟ Total weight of 34 students = 34 × 46.5 kg

➟ Total weight of 34 students = 1581 kg

Including teacher,

• So, the total number of people = 35 ( students + teacher )

Let,

• The weight of teacher is x

Note : We will convert 500 g into kg. So, the mean will be 0.5 kg.

$: \implies \bf{ \dfrac{1581 + x}{35} = 46.5 + 0.5}$

$: \implies \bf{ \dfrac{1581 + x}{35} = 47}$

$: \implies \bf{1581 + x = 1645}$

$: \implies \bf{x = 1645 - 1581}$

$:\implies{ \underline{ \boxed{\mathfrak \pink{x = 64 \: \sf \: kg}}}}$

Answer 2

$\Large\bf{\color{coral}GiVeN,}$

• The mean weight of a class of 34 students is 46.5 kg.

• If the weight of the teacher is included, the mean rises by 500 g.

$\Large\bf{\color{lime}To\:FiNd,}$

• The weight of the teacher.

$\Large\bf{\color{cyan}CaLcUlAtIoN,}$

$\longmapsto\:\:\bf\blue{Total\:weight\:=\:No.\:of\:students\times{Mean\:weight}\:}$

$\longmapsto\:\:\bf\blue{Total\:weight\:=\:34\times{46.5}\:}$

$\longmapsto\:\:\bf\blue{Total\:weight\:=\:1581\:kg\:}$

$\bf\red{According\:to\:the\:question}$

☆ New mean rises by 500 g, when the weight of the teacher is included.

$\green\bigstar\:\:\bf\orange{New\:mean\:=\:\dfrac{Total\:weight\:+\:Weight\:of\:teacher}{34\:+\:1}\:}$

$:\implies\:\:\bf{(46.5\:+\:0.5)\times{35}\:=\:1581\:+\:Weight\:of\:teacher\:}$

$:\implies\:\:\bf{47\times{35}\:=\:1581\:+\:Weight\:of\:teacher\:}$

$:\implies\:\:\bf{1645\:=\:1581\:+\:Weight\:of\:teacher\:}$

$:\implies\:\:\bf{Weight\:of\:teacher\:=\:1645\:-\:1581}$

$:\implies\:\:\bf\purple{Weight\:of\:teacher\:=\:64\:kg}$

$\Large\bold\therefore$ Weight of the teacher is 64 kg.