Question

Average age of 8 men increased by 2 years when two women is included in place of two men of ages 20 yrs and 24 yrs . find the average age of women

Answer 1

Let the average age of men be x.

• Average age of 8 men increased by 2 years when 2 person included.
• Excluded person's age are 20 yrs and 24 yrs.

→ x = (x₁ + x₂..xₙ)/n

→ x = (x₁ + x₂..x₈)/8

→ 8x = (x₁ + x₂..x₈) [1]

Finally, After included two women in place of two men of ages 20 yrs and 24 yrs.

Let the age of the two women be y₁ and y₂.

→ x + 2 = [(x₁ + x₂..x₈) -20-24+y₁+y₂]/8

→ x + 2 = [(x₁ + x₂..x₈) - 44 + y₁ + y₂]/8

→ x + 2 = [8x - 44 + y₁+y₂]/8

→ 8x + 16 = 8x - 44 + y₁+y₂

→ 16 + 44 = y₁ + y₂

→ 60 = (y₁ + y₂)

Now, It's time to find the average age of that two women.

→ (y₁ + y₂)/2

→ 60/2

→ 30

Hence,

The Average age of the women will be 30 years.