The ratio of age of A and B is x : y. If A's age is increased by 3 years

Ques - The ratio of age of A and B is x : y. If A's age is increased by 3 years and B's age is increased by 2 years then new ratio of their ages becomes 24: 25. Given that the sum of their actual ages is 93 years. Find the actual ratio of their ages.

(a) 21 : 22

(b) 42 : 45

(c) 45 : 48

(d) Can't determined

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