Question

The average age 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men . The average age of the two new men is _______________

• A. 22 years
• B. 24 years
• C. 28 years
• D. 30 years

Answer 1

The correct option is D 30 years

The average of the original 8 men is equal to x
This means that the sum of their ages divided by the number of men = x
we get, $S/8=x$
we know that if we subtract (21 and 23) from the sum, and we add the ages of 2 other men, that the average age now becomes (x+2).
formula for this would be:
$(S-44+y)/8=(x+2)$
y represents the sum of the ages of the 2 new men.
we have 2 equations:
$S/8=x$ and $(S-44+y)/8=(x+2)$
if we multiply both sides of each equation by 8, then we get:
$S=8\times x$ and $S-44+y=8\times (x+2)$
Since S = 8*x in the first equation we can substitute 8*x for S in the second equation to get:
$8\times x-44+y=8\times (x+2)$
$8\times x-44+y=8\times x+16$
we subtract 8*x from both sides of the equation and we add 44 to both sides of the equation to get:
$y=60$
y is the sum of the ages of the 2 new men.
their average age is 60/2 = 30
Answer (D) 30