The ratio of the age of Ajay and Atul is 4:5. After 5 years the ratio will be 5:6. Find the ratio of their age after 20 years.

Let's solve this step by step:

Step 1: Let's assume the present ages of Ajay and Atul are 4x and 5x respectively.

Step 2: According to the problem, after 5 years the ratio of their ages will be 5:6. So, we can write it as (4x+5)/(5x+5) = 5/6.

Step 3: Cross multiply to solve for x. We get 24x + 30 = 25x + 25.

Step 4: Simplify the equation to find the value of x. We get x = 5.

Step 5: Substitute x = 5 in the expressions of their present ages. So, Ajay's present age = 4x = 20 years and Atul's present age = 5x = 25 years.

Step 6: Now, we need to find the ratio of their ages after 20 years. So, Ajay's age after 20 years = 20 + 20 = 40 years and Atul's age after 20 years = 25 + 20 = 45 years.

Step 7: Therefore, the ratio of their ages after 20 years will be 40:45 or 8:9.