average

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The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years
are substituted by two women. The average age of these two women is:

[amising6]

The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years
are substituted by two women. The average age of these two women is:

now a shortcut based on logic
when two wommen were added average age of 8 member increased by 2 years i.e they added 2 years to each member age so total age added 2*8=16
now two men who left teir total age are 35+45=80
so age of women who replaced them must be 80+16=96
so average age of joining women =96/2=48

[Rahul@gurome]

Solution:
Let the average age of the 8 persons in the committee be x.
So total age is 8*x = 8x.
Let the total age of the two women substituted be y.
When the two men aged 35 and 45 are removed and the two women replaced in the committee, the total age is 8x - (35+45)+y = 8x - 80 + y.
So the new average age is (8x - 80 + y)/8 = x - 10 +y/8.
This is 2 more than original average age x.
So (x - 10 +y/8) - x = 2.
Or y/8 = 12.
Or y = 96.
We need the average age of the two women which is 96/2 = 48 years.

[selango]

Average=Sum of 8 peoples/8

A=(Sum of 6 peoples+35+45)/8

A=(Sum of 6 peoples+80)/8--Eqn1

2 women W1 and W2 replace 35 and 45 aged people.

A=(Sum of 6 peoples+W1+w2)/8

Sub A from eqn 1 above,

(Sum of 6 peoples+80)/8=(Sum of 6 peoples+W1+w2)/8

We will get W1+W2=96

Average of two women=96/2=48