Question

The average age in a tennis club dropped twice. Once when a member, Amit, moved away and next when a new member, Divya joined the club. The average age of the members in the club is around 35-45. Most members tend to join at an age of 25 and leave the club at age 55. The average leans towards the older members of the club. When a young Divya joined the club the average age dropped. The new club member joined in 2010 and the old member left in 2009. What was the age of the new member, who joined the tennis club, as of April 1, 2012?​

Answer 1

Step-by-step explanation:

Lets start with an example,

consider a,b and c and their age 1,2 and 3 respectively

Now their average age= 1+2+3/3= 2

when 1 moves out from that group

their new average= 2+3/2= 5/2= 2.5

and when 2 moves out, their average= 1+3/2= 4/2= 2

the result will differ when there are lots of members

but when 3 moves out, the new average= 1+2/2= 3/2=1.5

here we see that, if an oldest member moves out of the group the average decreases which is the case when Amit left the group ( he was around 45-55)

Now back to the example,

consider only 2 members are in a group

a and b with their age 1 and 2

so the average now is 1.5

when a new member c(2) moves in

we have 1+2+2/3= 5/3= 1.66

the average increases here ( may differ when there are more members)

now let's take c age as 1

we have 1+1+2/3= 4/3= 1.333

here we can see the age has decreased

so the age must be less than 2 for the average to drop.

And since 25 is the ideal age for joining

Divya age is less than 35

note: example is just for clearing concept, the answer is just as simple as ( if a member of age above average joins then the average increases and if below average joins the average decreases)