Math, asked by GrimReaper9604, 9 months ago

The mean age of 5 children of a family is 12 years. If four of them are respectively 6, 11, 13 and 16
years, find the age of the sixth child.

Answers

Answered by Anonymous

$<!DOCTYPE html><html><body><h1>Answer : </h1></body><html>$

Let the 5 th child's age be ' a '

According to the question :

Age of 4 children + Age of 5 th / Total number of children = 12 / 1

☞ 6 + 11 + 13 + 16 + a / 5 = 12 / 1

☞ 46 + a = 60

☞ a = 60 - 46

☞ a = 14.

Therefore the age of 5 th

child is 14.

Answered by nilesh102

Question:-

The mean age of 5 children's of a family is 12 years. If four of them are 6, 11, 13 and 16 years respectively. Find the age of the sixth child.

Solution:-

{ According to question }

Let, x be the fifth child & y be the sixth child.

{ According to question }

The mean age of 5 children's of family is 12 year.

Hence,

To find age of Fifth child

${ \bf{ \purple{\dashrightarrow}{ { \frac{sum \: of \: age\:of \: five \: children}{5} ={ \small{ mean \: age }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { \frac{6 + 11 + 13 + 16 + x}{5} ={ \small{ 12}}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { \frac{46 + x}{5} ={ \small{ 12 }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { 46 + x ={ \small{ 12 \times 5 }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { 46+ x ={ \small{ 60 }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { x ={ \small{ 60 - 46 }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { x ={ \small{ 14 \: year }}}}}}$

To find age of Sixth child

let, assume that the mean age of 6 children's of a family is 12 years.

Now,

${ \bf{ \purple{\dashrightarrow}{ { \frac{sum \: of \: age\:of \: six \: children}{6} ={ \small{ mean \: age }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { \frac{6 + 11 + 13 + 16 + 14 + y}{6} ={ \small{ 12 }}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { \frac{60 + y}{6} ={ \small{ 12}}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { 60 + y ={ \small{ 12 \times 6}}}}}}$

${ \bf{ \purple{\dashrightarrow}{ {60 + y={ \small{ 72}}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { y ={ \small{ 72 - 60}}}}}}$

${ \bf{ \purple{\dashrightarrow}{ { y ={ \small{ 12 \: year}}}}}}$

Hence age of Fifth child is 14 year's and age of Sixth child is 12 year's.

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