Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

To solve this problem, we can use the method of cross-multiplication in the concept of ratios.

Step 1: Let's denote the present ages of Kunal and Sagar as K and S respectively.

Step 2: According to the problem, six years ago, the ratio of Kunal's age to Sagar's age was 6:5. So, we can write this as (K-6)/ (S-6) = 6/5.

Step 3: The problem also states that four years from now, the ratio of their ages will be 11:10. So, we can write this as (K+4)/ (S+4) = 11/10.

Step 4: Now we have two equations, and we can solve them simultaneously.

By cross-multiplication, we get:

5*(K-6) = 6*(S-6) ----(equation 1)

10*(K+4) = 11*(S+4) ----(equation 2)

Solving these two equations will give us the present ages of Kunal and Sagar.

Step 5: Multiply equation 1 by 10 and equation 2 by 5, we get:

50*(K-6) = 60*(S-6) ----(equation 3)

50*(K+4) = 55*(S+4) ----(equation 4)

Subtract equation 4 from equation 3, we get:

5010 = 5S So, S = 100

Therefore, Sagar's present age is 100 years.