Tom Cruise

[Aman verma]

Q: Tom Cruise has only five people in his family :Tom , his wife ,a son and two daughters.Four years ago the age of his wife was 8 times that of his son and presently the sum of the ages of his younger daughter and his wife is same as the sum of the ages of Tom and his son.The average age of the family is .

I. The younger daughter's age is 4/5th of the elder daughter's age.

II.The age of the eldest daughter is 3/8 times that of her father Tom and the age of the son is 1/5th that of his father Tom.

[thephoenix]

Q: Tom Cruise has only five people in his family :Tom , his wife ,a son and two daughters.Four years ago the age of his wife was 8 times that of his son and presently the sum of the ages of his younger daughter and his wife is same as the sum of the ages of Tom and his son.The average age of the family is .

I. The younger daughter's age is 4/5th of the elder daughter's age.

II.The age of the eldest daughter is 3/8 times that of her father Tom and the age of the son is 1/5th that of his father Tom.

IMO B

[Pedros]

I know i have overlooked something so someone please correct me.....
we are looking for the value of ( F+W+S+Dy+De ) / 5.

using the 2 statmens together I concluded all family members age in terms of the father's age

De = 3/8 F
S = 1/5 F
Dy = 12/40 F
W= 8/5 F

but cant find 2 equations and 2 unknowns to solve for any specific family member age.

i will go for E

[harsh.champ]

Q: Tom Cruise has only five people in his family :Tom , his wife ,a son and two daughters.Four years ago the age of his wife was 8 times that of his son and presently the sum of the ages of his younger daughter and his wife is same as the sum of the ages of Tom and his son.The average age of the family is .

I. The younger daughter's age is 4/5th of the elder daughter's age.

II.The age of the eldest daughter is 3/8 times that of her father Tom and the age of the son is 1/5th that of his father Tom.

Hey pedros,
I tried doing this ques. and also looked up at ur post
Can you post the OA plz??
It will be helpful.
If my answer is right then I will post the soln. method.
Thanks

[Pedros]

Champ, I dont have the OA, maybe the original poster of the question does.

But thank you for taking time to give it a try.

[kstv]

If the age of the family is T for Tom, S for son, W for wife, De for elder daughter and Dy for younger daughter.

W - 4 = 8 (S-4)
T+S = W + De + Dy

1) 4 De = 5 Dy still too many unknowns
2) 3T = 8 De and T = 5 S

even with 1 & 2 the eq is not solvable. I suspect the two hints are not compatiable. There is a flaw in the Q. Love to be proven otherwise.

[ajith]

Q: Tom Cruise has only five people in his family :Tom , his wife ,a son and two daughters.Four years ago the age of his wife was 8 times that of his son and presently the sum of the ages of his younger daughter and his wife is same as the sum of the ages of Tom and his son.The average age of the family is .

I. The younger daughter's age is 4/5th of the elder daughter's age.

II.The age of the eldest daughter is 3/8 times that of her father Tom and the age of the son is 1/5th that of his father Tom.

Tom -t
Wife -w
son - s
Elder daughter - e
Younger daughter - y

w-4 = 8(s-4)
w= 8s-28
t+s = y + w
t+s = y + 8s-28
t = y+ 7(s-4) ---(1)

1) y = 4/5*e -- Not seeming to be sufficient

2) e =3/8 t ; t =5s -- Insufficient

Combining,

5s = 3/8*4/5*5s + 7(s-4)
5s = 3/2s +7s -28
3.5 s = 28

s = 8
t=40
e=15
y= 12
w = 36

One can find the average
[spoiler]
C, IMO[/spoiler]

[firdaus117]

Let ages in years be T,W,S,D and d of Tom,his wife,his son,his eldest daughter and youngest daughter respectively.
Given conditions,
W-4=8(S-4)
or, W=8S-28 ---------- (1)
Also, d+W=T+S ---------(2)
From I. d= 4/5 D insufficient
From II. D=3/8 T----(3)
S=1/5 T----(4)
Putting value of S from 4 in 1,
W=8/5 T-28---(5)
Putting the value of W from 5 in 2,
d=T+S-8/5T+28
=28 - 2/5 T----(6)
Now avg of family= Sum(T,W,S,D,d)/5
=An expression in T insufficient
Now combining both statements,
d=4/5 D
28 - 4/5 T=4/5 *3/8 T
or, T=40 years
Substitute it in avg family expression,we can get the average.
Hence, both statements needed to find the average.

[kstv]

Thanks I see my mistake
I wrote T + S = W + De + Dy
T+S = W + Dy
Putting the value of Tom Cruise as 40, close to his actual age I was able to get their respective age. But the above wrong eq. was my undoing.

[Aman verma]

Ans[spoiler]c)[/spoiler] Ajith's method and Firdaus117's method is quite amazing.Better than mine .