Ken is 20 years older than his niece. 2 years from now, his niece will be
12 of his age while his cousin will be
25 of his niece. Express his cousin’s present age as a fraction of Ken's present age. Leave your answer in its simplest form.
| |
Ken |
Ken's niece |
Ken's cousin |
Difference between
Ken and Ken's niece |
| Before |
10 u - 2 |
5 u - 2 |
2 u - 2 |
20 |
| Change |
+ 2 |
+ 2 |
+ 2 |
|
After
|
2x5 |
1x5 |
|
|
| |
5x1 |
2x1 |
|
Comparing Ken, his niece and his cousin
in the end |
10 u |
5 u |
2 u |
5 u |
The repeated identity is the age of Ken's niece. LCM of 1 and 5 is 5.
The difference in age between Ken and Ken's niece remains unchanged.
Difference in age between Ken and Ken's niece
= 10 u - 5 u
= 5 u
5 u = 20
1 u = 20 ÷ 5 = 4
His cousin's present age
= 2 u - 2
= 2 x 4 - 2
= 8 - 2
= 6
Ken's present age
= 10 u - 2
= 10 x 4 - 2
= 40 - 2
= 38
His cousin's present age as a fraction of Ken's present age
=
638=
319 Answer(s):
319 
