**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