Question

Out of a total of 10 students, the average weight of 9 students is 60 kg. If the weight of the 10th students is 9 kg more than the average weight of all the 10 students, then the weight of the 10th student would be:

Answer 1

Average weight = 60 kg

No of students = 9

Weight of the 10th student = 9kg more than the average weight of the 10 students.

Average weight of 9 students = 60 kg.

Total weight of 9 students = 60 x 9 = 540 kg.

total weight of 10 students = 540 + x (let the 10th student weight be x)

Average weight of 10 students =

540 + x/10

Weight of 10th student = 9 + 540 + x /10

x =

$9 + \frac{540 + x}{10}$

x - 9 = 540 + x/10

10x - 90 = 540 + x

10x - x = 540 + 90

9x = 630

x = 70 kg.

Weight of the 10th student is 70 kg.

Answer 2

Step-by-step explanation:

⠀

$\setlength{\unitlength}{2mm}\begin{picture}(8,2)\linethickness{0.4mm}\put(20,10){\dashbox{0.01}(25,15)}\put(45,10){\dashbox{0.01}(5,25)}\multiput(18,10)(0,20){2}{\line(2,0){35}}\multiput(52,30)(0,4){2}{\line(0,2){1}}\multiput(20,8)(19,0){2}{\line(2,0){6}}\put(28,7.5){\large\sf{9 Students}}\put(46,7.5){\large\sf{10th}}\put(15,25){\large\sf{60 kg}}\put(15,31){\large\sf{Original Average = 60 + 1 = 61}}\put(51,32){\large\sf{9 kg more}}\put(25,27){\sf{ \dfrac{\sf9\:kg\:more}{\sf9\:students} = 1 each}}\end{picture}$

⠀

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Avg_{10\:Students}=Avg_{9\:Students}+Inc.\:in\:Avg.\\\\\\:\implies\sf Avg_{10\:Students} = 60 \:kg+\dfrac{\sf9\:kg\:more}{\sf9\:students}\\\\\\:\implies\sf Avg_{10\:Students} = 60 \:kg + 1\:kg\\\\\\:\implies\sf Avg_{10\:Students} =61 \:kg$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Weight of the 10th Student :}}$

$\dashrightarrow\sf 10th\:Student=Avg_{10\:Students}+9\:kg\\\\\\\dashrightarrow\sf 10th\:Student=61\:kg+9\:kg\\\\\\\dashrightarrow\underline{\boxed{\sf 10th\:Student=70\:kg}}$

⠀

$\therefore\:\underline{\textsf{Weight of the 10th student is \textbf{70 kg}}}.$