Four years ago, the average age of a family of 9 members was 31 years.

Question

Four years ago, the average age of a family of 9 members was 31 years. Two years later a man died at an age of 41 years, what is the present average age of the family?

(A) 32
(B) 33
(C) 34
(D) 35
(E) 36

CareerGeek · Accepted Answer

Four years ago, the average age of a family of 9 members was 31 years

two years later, average of 9 members = 33 years
--> Total age = 33*9 = 297 years

A man of age 41 died two years ago.
--> So total age of 8 members = 297 - 41 = 256 years
--> Average age of 8 members 2 years ago (after death) = 256/8 = 32 years

So, Present average age = 32 + 2 = 34 years

IMO Option C.

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Archit3110 · Answer

total sum of ages = 31*9 ; 279
after 2 years ; increas +18 ; 297
41 years man dies ; so new total ; 256
then 16 to be added for 8 memers 2 year s; 272
avg of 8 people; 272/8 ; 34 yrs
IMO C

ScottTargetTestPrep · Answer

If the man had still been alive two years later, the sum of their ages would have been 9 x 33 = 297. However, since the man is dead, the sum of the remaining 8 people’s ages two years ago was 297 - 41 = 256, and therefore, their average age two years ago was 256/8 = 32. Since the age of every surviving member will increase by 2, the average age will increase by 2 as well, and thus, their present average age is 34.

Alternate Solution:

The sum of the ages of the 9 members is 31 x 9 = 279. The man who died two years ago was 39 years old four years ago. Thus, without the man, the sum of the ages of the remaining 8 members four years ago was 279 - 39 = 240. In four years, the age of every member will increase by 4; therefore the total age will increase by 8 x 4 = 32. Thus, in the present time, the sum of the ages of the surviving members is 240 + 32 = 272 and the average age is 272/8 = 34.

Answer: C

TarunKumar1234 · Answer

4 years ago total age = 31*9 = 279 years
Since, we are talking about 2 years, some one passed away, so Now, total age = 279 +9*2 - 41 = 256 years
Average age = 256/8 = 32 years

Now, 2 years later = present time average age = 32 +2 = 34.

So, I think C.

MathRevolution · Answer

Four years ago, let 7 members were of 31 years, 1 member was 39 years and 1 member was of 23 years. Hence, the average was 31 years.

Two years later, a man died at an age of 41. Therefore, 8 members are left.

So remaining 7 members will be of 31 + 2 = 33 years and 1 member of 23 years will be of 25 years.

Present age : ( 2 more years added to each): 7 members are of 35 years now and 1 member is of 27 years.

The present average could have been 35 but 1 member is short of 8 years and this 8 years difference will reduce the average by 1 as there is a total of 8 members. Hence present average is 35 - 1 = 34 years.

Answer C

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Four years ago, the average age of a family of 9 members was 31 years.

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Four years ago, the average age of a family of 9 members was 31 years.

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