Age Problem Analysis

Let Kamal's present age be $K$ years and Sunil's present age be $S$ years.

Formulating Equations

We translate the given information into algebraic equations:

• "Six years hence Sunil will be twice as old as Kamal":

  Sunil's age in 6 years: $S + 6$

  Kamal's age in 6 years: $K + 6$

  Equation 1: $S + 6 = 2(K + 6)$

• "Two years ago he was four times as old as Kamal":

  Sunil's age 2 years ago: $S - 2$

  Kamal's age 2 years ago: $K - 2$

  Equation 2: $S - 2 = 4(K - 2)$

Simplifying Equations

Simplify the two equations:

• From Equation 1: $S + 6 = 2K + 12 \implies S = 2K + 6$
• From Equation 2: $S - 2 = 4K - 8 \implies S = 4K - 6$

Solving for Kamal's Age

Since both expressions equal $S$, we set them equal to each other to solve for $K$:

$2K + 6 = 4K - 6$

Subtract $2K$ from both sides: $6 = 2K - 6$

Add 6 to both sides: $12 = 2K$

Divide by 2: $K = 6$

Conclusion

Kamal's present age is 6 years.