Five years ago, Ahsan's age was 7 times Shakeel’s. After 3 years, Ahsan’s age will be 3 times Shakeel’s. What is Ahsan’s current age?

Five years ago, Ahsan's age was 7 times Shakeel’s. After 3 years, Ahsan’s age will be 3 times Shakeel’s. What is Ahsan’s current age?

Explanation

Let current ages be:

  • Ahsan =
    A

  • Shakeel = SS

Condition 1 (Five years ago):

Condition 2 (Three years later):


A + 3 = 3(S + 3) quad text{(Equation 2)}


Solving the equations:

From Equation 1:


A - 5 = 7S - 35 Rightarrow A = 7S - 30 quad text{(Equation 3)}

Substitute into Equation 2:


(7S - 30) + 3 = 3(S + 3) Rightarrow 7S - 27 = 3S + 9 Rightarrow 7S - 3S = 9 + 27 Rightarrow 4S = 36 Rightarrow S = 9

Now, plug back to find Ahsan's age:

A = 7S - 30 = 7(9) - 30 = 63 - 30 = 33