Question

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

Answer 1

Step-by-step explanation:

Average = sum/number *of quantities.

Here,

=> Average weight = (sum of weight of 9 sts)/9

=> 60 = (sum of weight of 9 students)/9

=> 540 = sum of weight of 9 students

Let the average weight of 10 students be 'a'.

So, as said,

Weight 10th student = a + 9

Thus,

=> average weight of 10 students = a

=> (weight of 9 students + 10th stude.) = a

=> (540 + a + 9)/10 = a

=> 549/10 + a/10 = a

=> 54.9 = a - 0.1a

=> 54.9 = 0.9a

=> 54.9/0.9 = a

=> 61 = a

=> 61+9 = a +9 = weight of 10th student

=> 70 = weight of 10th studenta

Answer 2

Answer:

• Total Students = 10
• Average of 9 Students = 60 kg
• Weight of 10th Student is 9 kh more than Average weight of all 10 Students.
• Find Weight of 10th Student.

⠀

If we can find Average of all 10 students, then we can calculate weight of 10th student easily. (By Adding 9 kg to it) i.e. Given above.

⠀

Average of 9 Students is 60 kg.

Weight of 10th Student exceed by 9 kg of Average of all 10 students weight.

That 9 kg is excess over Average Weight. Hence it will be distributed among all Students excluding 10th Student. Hence it will Increase Average by :

⠀

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

⠀

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

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

$\rule{180}{1.5}$

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

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

⠀

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