Question

the average age of a group of people decreased by 2 years when one 80 year old person got replaced by two persons aged 40 years and 38 years. the average age then got increased by 1 when a 42 year old joined. the number of people in the group is​

Answer 1

Answer:

14 people

Step-by-step explanation:

Av. age= Sum of ages/ Number of people = s/n

As per given, after first change in the group:

• s/n - 2 = (s-80+40+38)/(n-1+2)
• s/n - 2= (s-2)/(n+1)
• (s-2n)/n=(s-2)/(n+1)
• (s-2n)(n+1)=n(s-2)
• sn+s-2n²-2n=sn-2n
• s=2n²

Next change in the group reflected as:

• (s-2)/(n+1)+1 = (s-2+42)/(n+1+1)
• (s-2+n+1)/(n+1) = (s+40)/(n+2)
• (s+n-1)/(n-1) = (s+40)/(n+2)
• (s+n-1)(n+2) = (s+40)(n+1)
• sn+2s+n²+2n-n-2= sn+s+40n+40
• n²-39n+s-42=0   ---- replacing s with 2n² from previous equation
• n²-39n+2n²-42=0
• 3n²-39n-42=0

• n²-13n-14=0

Solving quadratic equation we get integer solution of:

• n=14

Answer: number of people in the group is 14

Answer 2

Answer:

Step-by-step explanation: