Alisha's father was 7 time older to her 18 years ago. He would be 2 times of…
2024
Alisha's father was 7 time older to her 18 years ago. He would be 2 times of her age 2 years from now. Six years ago, what was ratio of Alisha's age to her father ?
- A.
2:5
- B.
1:3
- C.
3:5
- D.
2:3
Attempted by 8 students.
Show answer & explanation
Correct answer: A
Let present ages of Alisha and her father be A and F respectively.
From 18 years ago: F - 18 = 7(A - 18)
From 2 years from now: F + 2 = 2(A + 2)
Solve the two equations. From the first: F = 7A - 108
From the second: F = 2A + 2
Equate the expressions for F: 7A - 108 = 2A + 2
Solve for A: 5A = 110 ⇒ A = 22
Find F using F = 2A + 2: F = 46
Six years ago their ages were 16 (Alisha) and 40 (father).
Ratio six years ago: 16:40 = 2:5
Final Answer: 2:5