​The ratio of the sums of money Arun and Ahaan had is 9 : 5. If Arun gives ₹12 from his share to Ahaan, then the ratio will change to 4 : 3. How much money did Arun have initially? ​

Correct option is C

Given:​ 

Ratio of the sums of money Arun and Ahaan = 9 : 5

Arun gives ₹12 from his share to Ahaan, ratio will change to 4 : 3.

Solution:

Let's assume:

Arun's initial money = 9x

Ahaan's initial money = 5x

After Arun gives ₹12 to Ahaan:

Arun's money = 9x - 12

Ahaan's money = 5x + 12

Now, the ratio becomes 4:3, so:

​$$\frac{9x - 12}{5x + 12} = \frac{4}{3}$$​​

3(9x - 12) = 4(5x + 12)

27x - 36 = 20x + 48

27x - 20x = 48 + 36

7x = 84

x = 12

Therefore, Arun's initial money was 9x = 9 $$\times$$​12 = ₹108.

Option (c) is right answer.