The age of Mathi is 120% of the age of Sunil and the ratio of the age of Sunil to Bala is 5:8.If the age of Mathi 5 years hence is equal to the age of Bala 5 years ago, then find the age of Sunil?

Sure, let's solve this step by step:

Step 1: Let's assume the age of Sunil as 'x' years.

Step 2: According to the problem, Mathi's age is 120% of Sunil's age. So, Mathi's age is 1.2x years.

Step 3: The ratio of the age of Sunil to Bala is 5:8. So, if Sunil's age is 5 parts, Bala's age is 8 parts. Let's assume the common ratio as 'y'. So, Sunil's age is 5y and Bala's age is 8y.

Step 4: According to the problem, Mathi's age 5 years hence (1.2x + 5) is equal to Bala's age 5 years ago (8y - 5).

Step 5: Now, we have two equations (x = 5y and 1.2x + 5 = 8y - 5) and two variables (x and y). We can solve these equations to find the values of x and y.

Step 6: Substitute x = 5y in the second equation, we get 1.2*5y + 5 = 8y - 5.

Step 7: Simplify the equation, we get 6y + 5 = 8y - 5.

Step 8: Rearrange the equation, we get 8y - 6y = 5 + 5.

Step 9: Simplify further, we get 2y = 10.

Step 10: Solve for y, we get y = 10/2 = 5.

Step 11: Substitute y = 5 in the first equation (x = 5y), we get x = 5*5 = 25.

So, the age of Sunil is 25 years.