Age

[Imsukhi]

A father is three times as old as his son. The product of fathers age and son,s age 3 years ago is 16 Times the present age of the son.
What is fathers age..?

24
25
27
29


Pls equate

[usmabama]

This is how I set it up:

The problem tells us F=3S and (F-3)(S-3)=16S

FS-3F-3S+9=16S

We can also plug 3S in for F because that was given to us, so:

3S^2-9S-3S+9=16S
3S^2-28S+9=0
(3S-1)(S-9)

So S can only equal 9.
Plug that into the original equation and F=3(9)=27
It checks out for the other equation too
(27-3)(9-3)=16(9)
(24)(6)=16(9)...reduce to make it easier
(3)(2)=(2)(3)...
Answer=27

[Brent@GMATPrepNow]

A father is three times as old as his son. The product of fathers age and son,s age 3 years ago is 16 Times the present age of the son.
What is fathers age..?
24
25
27
29
Pls equate

A father is three times as old as his son.
On GMAT age problems, the ages of the individuals are typically integers.
So, we can expect the father's age to be a multiple of 3.
Since only 24 and 27 are multiples of 3, we can eliminate the other answers and just test 24 and 27 and see which one works.

Cheers,
Brent

[Brent@GMATPrepNow]

The product of father's age and son's age 3 years ago is 16 Times the present age of the son.

By the way, the wording here is somewhat ambiguous.
Does 3 years ago refer to the son's age only, or both the son's age AND the father's age?
So, we have two possible scenarios:
1) The product of father's current age and son's age 3 years ago . . . .
2) The product of father's age 3 years ago and son's age 3 years ago . . . .

Cheers,
Brent