Question

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

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

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.

Answer 2

Answer:

Mean weight of 34 students = 46.5kg So the total weight = 34 (46.5) = 1581kg We know that Mean weight of 34 students and teacher = 46.5 + 0.5 = 47kg So the total weight of 34 students and teacher = 47 (35) = 1645kg The weight of teacher = Weight of 34 students and teacher – total weight By substituting the values Weight of the teacher = 1645 – 1581 = 64kg Therefore, the weight of the teacher is 64 kg