sgr21 wrote:The age of John 21 years from now will be half that of Parson at that time. Currently the ratio of John's age to Parson's age is 5:17. What was the age of Parson 2 years ago?
(A) 15 years
(B) 49 years
(C) 32 years
(D) 11 years
One approach is to
test the answer choices, and see which one works. In fact, I suspect this might be the fastest approach.
I'll leave you to try that approach. Here's the algebraic approach.
Let J = John's
present age
Let P = Parson's
present age
21 years in the future
J + 21 = John's age
P + 21 = Parson's age
The age of John 21 years from now will be half that of Parson at that time
So, John's age = (Parson's age)/2
In other words, J + 21 = (P + 21)/2
Multiply both sides by 2 to get: 2(J + 21) = P + 21
Simplify:
2J - P = - 21
Currently the ratio of John's age to Parson's age is 5:17
So, J/P = 5/17
Cross multiply to get: 17J = 5P
Simplify:
17J - 5P = 0
From here, if we solve this system . . .
2J - P = - 21
17J - 5P = 0
. . . we get P = 51, which means Parson's
present age is 51.
So, 2 years ago, he was
49
Answer:
B
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
