At present, A is thrice as old as B. C is 5 years elder 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:

Options
a) 1 : 5
b) 4 : 7
c) 1 : 4
d) 2 : 3

Solution

As per question
A = 3B
C = B + 5
A + B + C = 75
3B + B + B + 5 = 75
5B + 5 = 75
5B = 70
B = 14
A = 3 x 14 = 42
C = 14 + 5 = 19
Age of B 5 years ago
B = 14 – 5 = 9
Age of A after 3 years
A = 43 + 3 = 45
The ratio of the age of B five years ago to the age of A three years from now will be
B : A = 9 : 45
B : A = 1 : 5

Answer: a) 1 : 5