Question

The mean age of 6 person is 14.5 years . the mean age of four of them is 13.25 year. If the age of fifth person is 16 years. Find the age of the sixth​

Answer 1

Answer:

Total age of first four people = 53

Average age of all people = 14.5 × 6

= (53 + 16 + x)/6

69 + x = 87 × 6

x

Answer 2

The age of the sixth​ person is "18 years".

Step-by-step explanation:

Let $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$, and $x_{6}$ be the age of six person.

∴ The mean age of 6 person = 14.5 years

∴ $x_{1}$ + $x_{2}$ + $x_{3}$ + $x_{4}$ + $x_{5}$ + $x_{6}$  = 14.5 × 6

⇒  $x_{1}$ + $x_{2}$ + $x_{3}$ + $x_{4}$ + $x_{5}$ + $x_{6}$  = 87   .... (1)

Also,

$x_{1}$ + $x_{2}$ + $x_{3}$ + $x_{4}$ = 13.25 × 4

⇒ $x_{1}$ + $x_{2}$ + $x_{3}$ + $x_{4}$ = 53 ...

(2)

Putting the value of (2) in (1), we get

53 + $x_{5}$ + $x_{6}$ = 87

⇒ 53 + 16 + $x_{6}$ = 87 [Since, the age of fifth person = 16 years]

⇒  $x_{6}$ = 87 - 69 = 18

Hence, the age of the sixth​ person is 18 years.