Gem will be 62 years old in 20 years' time. Now, Cathy's age is 23 of Gem's age. What was Cathy's age when she was 6 years less than 75% of Gem's age?
| |
Cathy |
Gem |
Difference |
| Before |
3 p - 6 |
4 p |
1 p + 6 |
| Change 1 |
+ ? |
+ ? |
|
| After 1 (Now) |
2 u |
3 u |
1 u |
| Change 2 |
+ 20 |
+ 20 |
|
| After |
2 u + 20 |
62 |
|
Gem's age in 20 years' time = 3 u + 20
3 u + 20 = 62
3 u = 62 - 20
3 u = 42
1 u = 42 ÷ 3 = 14
Difference between Gem's age and Cathy's age
= 1 u
= 14
75% =
75100 =
34 Difference in Gem's age and Cathy's age at first
= 4 p - (3 p - 6)
= 1 p + 6
The difference in age between Gem and Cathy remains unchanged.
1 p + 6 = 14
1 p = 14 - 6 = 8
Cathy's age when she was 6 years less than 75% of Gem's age
= 3 p - 6
= 3 x 8 - 6
= 24 - 6
= 18
Answer(s): 18
