At present, A is thrice as old as B. C is 5 years older than B. The sum of the ages of A, B, C is 75 years. The ratio of the age of B five years ago to the age of A three years from now is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 1 : 5.
Let the age of A, B, and C be x, y, z
Given that,
A is thrice as old as B, i.e., x = 3y......(1)
C is 5 years older than B, i.e., z = y + 5.....(2)
The sum of the ages of A, B, and C is 75, i.e., x + y + z = 75.....(3)
Put x = 3y and z = y + 5 in eqn 3
⇒ x + y + z = 75
⇒ 3y + y + (y + 5) = 75
⇒ 5y + 5 = 75
⇒ 5y = 70
⇒ y = 14
So, B's current age is 14 years, and A's current age is 42 years, and C's current age is 19 years
Now,
B's age five years ago = 14 − 5 = 9
A's age three years from now = 42 + 3 = 45
Thus,
Required ratio = 9/45 = 1/5 = 1 : 5