Finding the Present Ages of Nuri and Sonu

Video Explanation

Question

Five years ago, Nuri was three times as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Find their present ages.

Solution

Step 1: Let the Variables

Let present age of Nuri = \(x\) years

Let present age of Sonu = \(y\) years

Step 2: Form the Equations

Five years ago:

\[ x – 5 = 3(y – 5) \]

\[ x – 5 = 3y – 15 \]

\[ x – 3y = -10 \quad (1) \]

Ten years later:

\[ x + 10 = 2(y + 10) \]

\[ x + 10 = 2y + 20 \]

\[ x – 2y = 10 \quad (2) \]

Step 3: Solve by Elimination Method

Subtract equation (1) from equation (2):

\[ (x – 2y) – (x – 3y) = 10 – (-10) \]

\[ x – 2y – x + 3y = 20 \]

\[ y = 20 \]

Step 4: Find the Value of x

Substitute \(y = 20\) in equation (2):

\[ x – 2(20) = 10 \]

\[ x – 40 = 10 \]

\[ x = 50 \]

Conclusion

Present age of Nuri:

\[ \boxed{50 \text{ years}} \]

Present age of Sonu:

\[ \boxed{20 \text{ years}} \]