Question

the average age of 4 players is 20 years. If the age of coach is included. The average is increased increased by 20%.The age of coach is​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given :-

• The average age of 4 players is 20 years.
• If the age of the coach is included, the average is increased by 20%

To find :-

• The age of the coach.

According to the question,

Let the ages of the 4 players be x,y,z and k respectively.

Average :-

$\dfrac{sum \: of \: observations}{number \: of \: observations}$

$\dfrac{ x + y + z + k }{4} = 20$

Therefore,

By transposing 4 to the RHS (Right Hand Side),

$x + y + z + k = 20 \times 4$

$x + y + z + k = 80$

If the age of the coach is added, the average increases by 20%

Hence increase :

$\dfrac{20}{100} \times 20$

$= \dfrac{400}{100}$

$\dfrac{4 \not0 \not0}{1 \not0 \not0}$

$= 4$

Therefore the average increases by 24.

Let the coaches age be c.

New average when the coaches age is added :

$\dfrac{ x+y + z + k + c }{5} = 24$

as we already know that, x + y + z + k = 80,

Substituting the values,

$\dfrac{80 + c}{5} = 24$

By transposing 5 to the RHS (Right Hand Side)

$80 + c = 24 \times 5$

$80 + c = 120$

Transposing 80 to the RHS (Right Hand Side),

$c = 120 - 80$

$c = 40$

Hence the coach's age is 40.

Verification :-

Substituting c for 40,

$\dfrac{x + y + z + k + c}{5} = 24$

$\dfrac{80 + 40}{5} = 24$

$\dfrac{120}{5} = 24$

By cancelling,

LHS = RHS

hence verified