Question

their is a group of 19 people. the average weight of the first 10 people and last 10 people is 43 KG and 56 KG respectively. Given that the average weight
of all the people is 50 KG, find the weight of the 10th person

Answer 1

Answer:

the correct answer is 40kg.

Step-by-step explanation:

first 10 peoples weight is 430 kg. and last 10 peoples weight is 560kg.

all peoples weight is 19*50=950kg.

first 10 peoples weight is now substrate from all weight of the peoples

then we can find out last 9 peoples weight

950kg.-430kg.=520kg.

the weight is last 9 peoples weight

last 10 peoples weight is 560 kg.

last 9 peoples weight is 520 kg.

then 10 people weight is 560-520 =40 kg.

ans.

Answer 2

Given:

Total no. of people = 19

Average weight of all people = 50 kg

Average weight of first 10 people = 43 kg

Average weight of last 10 people = 56 kg

To find:

Weight of 10th person.

Solution:

Let w₁, w₂, w₃....w₁₉ be the weights of 19 people.

Average weight of 19 people = 50

Average = Sum/Total number

$\frac{w_{1}+w{2}+...+w_{19}}{19} =50$

$w_{1}+w_{2}+...+w_{19} =50*19=950...(1)$

Average weight of first 10 people = 43

$\frac{w_{1}+w{2}+...+w_{10}}{10} =43$

$w_{1}+w_{2}+...+w_{10} =10*43=430...(2)$

Subtracting equation (2) from (1)

$w_{11}+w_{12}+...+w_{19}=520...(3)$

This is the sum of weights of last nine people

Average weight of last 10 people = 56

$\frac{w_{10}+w_{11}+...+w_{19}}{10}=56$

$w_{10}+w_{11}+...+w_{19}=56*10=560...(4)$

Subtract equation (3) from equation (4) to determine the weight of 10th person.

$w_{10}=560-520=40kg$

The weight of the 10th person is 40kg.