Question

. The average age of a group of men is 20 years. If x

men whose average age is k years join the group,

the average age of the group would be y years. If x

men in the group whose average age is k years leave

the group, the would by y years. Find the value of

k.

(a) 15 (b) 20

(c) 25 (d) 23

​

Answer 1

Answer:

The average age of a group of 5 students was 10 the average age increased by 4 years when 2 new students joined the group what is the average age of the two new students who joined the group

Answer 2

Answer:

The value of k is 20

Step-by-step explanation:

Given the average of a group of men is 20

Let the number of men be 'n'

We know that average age = $\frac{Sum of age of all men}{No. of men}$

=> Sum of ages of all men = Average age * No. of men

                                            = 20*n

Given that when x men with average age k years join the group, the average age of the group becomes y.

We know that average age = $\frac{Sum of age of all men}{No. of men}$

=>Here,

Sum of ages of all men = Average age * No. of men

                                            = k*x

Therefore, the new group average becomes,

average age = $\frac{Sum of age of all men}{No. of men}$

=>           y      = $\frac{20n+kx}{n+x}$                               --(i)

Given that when x men with average age k years leave the group, the average age of the group becomes y.

We know that average age = $\frac{Sum of age of all men}{No. of men}$

=>Here,

Sum of ages of all men = Average age * No. of men

                                            = k*x

Therefore, the new group average becomes,

average age = $\frac{Sum of age of all men}{No. of men}$

=>           y      = $\frac{20n-kx}{n-x}$                           --(ii)

Equating equation (i) and (ii), we get,

$\frac{20n+kx}{n+x}$   =  $\frac{20n-kx}{n-x}$  

=> (20n+kx)(n-x) =  (20n-kx)(n+x)

=> 20n²-20nx +knx - kx² = 20n² + 20nx -knx -kx²

=> -20nx +knx =  20nx -knx

As n and x is common to both left and right hand side, we can cancel it.

=> -20n + k = 20 - k

=> k + k = 20 + 20

=> 2k = 40

=> k = 40/2

=> k = 20

Therefore, the value of k is 20