Mother and daughter

AIM TO CRACK GMAT wrote:A Mother’s age after 6 years will be thrice the age of her daughter now. The sum of their ages 6 years ago was 42. What is the ratio of the current ages of the mother and the daughter?

(A) 18:7 (B) 7:5 (C) 6:1 (D) 13:5


D

One approach is to test the answer choices, and see which one works.

Here's the algebraic approach:

Let M = mother’s present age
Let D = daughter's present age

6 years in the future
M + 6 = mother’s age

Mother’s age after 6 years will be thrice the age of her daughter now.
Presumably, this means that, in 6 years, the mom's age will be 3 times the daughter's current age.
So, (mother's age in 6 years) = 3(daughter's present age)
M + 6 = 3D
Simplify: 3D - M = 6


6 years ago
M - 6 = mother’s age
D - 6 = daughter’s age
The sum of their ages 6 years ago was 42.
So, (M - 6) + (D - 6) = 42
Simplify: D + M = 54

From here, if we solve this system . . .
3D - M = 6
D + M = 54

. . . we get D = 15 and M = 39,

What is the ratio of the current ages of the mother and the daughter?
mother's age : daughter's age = 39 : 15
= [spoiler]13 : 5[/spoiler]

Answer: D

Aside: If anyone is interested, we have a free video on solving GMAT age problems: https://www.gmatprepnow.com/module/gmat- ... ems?id=908
Cheers,
Brent