The average age of board of directors of a company having 15 directors...
Before Death = 48*15 = 720
The age of late director at the time of his death
720 - (56+x) + 36 + 14 = 672
X = 42
View all questions of this test
The average age of board of directors of a company having 15 directors...
Before Death = 48*15 = 720
The age of late director at the time of his death
720 - (56+x) + 36 + 14 = 672
X = 42
The average age of board of directors of a company having 15 directors...
Given:
- The company had 15 directors and the average age was 48 years.
- One director aged 56 resigned and another director died on the same day.
- A new director aged 36 joined the board.
- Next year, the average age of all 14 directors was 48 years.
To find: The age of the late director at the time of his death.
Solution:
Let's first find the sum of ages of all 15 directors before any changes occurred.
15 directors x 48 years = 720 years
This means the total age of all directors was 720 years.
After the changes occurred:
- One director aged 56 resigned, so we subtract 56 from the total age.
720 - 56 = 664
- Another director died on the same day, so we subtract that director's age as well.
664 - x = 2(14) [since there are now 14 directors left]
664 - x = 28
x = 636
The age of the deceased director was 636 years.
A new director aged 36 joined the board, so we add 36 to the total age.
636 + 36 = 672
Next year, the average age of all 14 directors was 48 years. This means the total age of all directors was:
14 directors x 48 years = 672 years
So, the sum of ages of all directors after the changes is also 672 years.
We can set up an equation to find the age of the deceased director:
(636 - age of the deceased director) + 36 = 672
Solving for the age of the deceased director:
600 + age of the deceased director = 672
age of the deceased director = 72
Therefore, the age of the late director at the time of his death was 72 years.
Answer: Option (B) 42 years.