Solution -
The ratio of age of A and B = x : y
The sum of their actual ages = 93 years
x + y = 93
x = 93 - y ___________ (1)
Now,
If A's age is increased by 3years and B's age is increased by 2 years then new ratio of their ages becomes 24: 25.
(x + 3) : (y + 2) = 24 : 25
(x + 3)/(y + 2) = 24/25
25(x + 3) = 24(y + 2)
25x + 75 = 24y + 48
25x - 24y = 48 - 75
25x - 24y = -27 ___________ (2)
From eq. (1) and eq. (2), we get
25x - 24y = -27
25(93 - y) - 24y = -27
2325 - 25y - 24y = -27
2325 - 49y = -27
- 49y = -27 - 2325
-49y = -2352
y = 2352/49
y = 48 _____________ (3)
Put the value of y in eq. 1
x = 93 - y
x = 93 - 48
x = 45
Therefore,
The actual ratio of their ages is 45 : 48.
Hence,
The correct answer is option (c) 45 : 48.
Thank You