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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?

Question

What is the present age of Sagar?

The total of the ages of Jiya, Kunal and Sagar is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4.

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Solution

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.

This problem has been solved

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