he total of the ages of Jiya, Kunal and Sagar is93 years. Ten years ago, the ratio of their ages was2 : 3 : 4. What is the present age of Sagar?

Let's solve the problem step by step:

Step 1: Let's assume the present ages of Jiya, Kunal, and Sagar as J, K, and S, respectively.

Step 2: According to the given information, the total of their ages is 93 years. So, we can write the equation as J + K + S = 93.

Step 3: Ten years ago, the ratio of their ages was 2:3:4. Let's calculate their ages ten years ago.

• Jiya's age ten years ago = J - 10
• Kunal's age ten years ago = K - 10
• Sagar's age ten years ago = S - 10

Step 4: According to the given ratio, we can write the equation as (J - 10) : (K - 10) : (S - 10) = 2 : 3 : 4.

Step 5: Now, we have two equations:

• J + K + S = 93
• (J - 10) : (K - 10) : (S - 10) = 2 : 3 : 4

Step 6: We can solve these equations to find the values of J, K, and S.

Step 7: Simplifying the second equation, we get (J - 10) / (K - 10) = 2/3 and (J - 10) / (S - 10) = 2/4.

Step 8: Cross-multiplying, we get 3(J - 10) = 2(K - 10) and 4(J - 10) = 2(S - 10).

Step 9: Expanding, we get 3J - 30 = 2K - 20 and 4J - 40 = 2S - 20.

Step 10: Simplifying further, we get 3J - 2K = 10 and 4J - 2S = 20.

Step 11: Now, we have a system of equations:

• J + K + S = 93
• 3J - 2K = 10
• 4J - 2S = 20

Step 12: We can solve this system of equations to find the values of J, K, and S.

Step 13: Solving the system of equations, we find J = 25, K = 36, and S = 32.

Step 14: Therefore, the present age of Sagar is 32 years.