Finding the Present Ages of Salim and His Daughter

Video Explanation

Question

Two years ago, Salim was three times as old as his daughter. Six years later, he will be four years older than twice her age. Find their present ages.

Solution

Step 1: Let the Variables

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

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

Step 2: Form the Equations

Two years ago:

\[ x – 2 = 3(y – 2) \]

\[ x – 2 = 3y – 6 \]

\[ x – 3y = -4 \quad (1) \]

Six years later:

\[ x + 6 = 2(y + 6) + 4 \]

\[ x + 6 = 2y + 12 + 4 \]

\[ x + 6 = 2y + 16 \]

\[ x – 2y = 10 \quad (2) \]

Step 3: Solve by Elimination Method

Subtract equation (1) from equation (2):

\[ (x – 2y) – (x – 3y) = 10 – (-4) \]

\[ x – 2y – x + 3y = 14 \]

\[ y = 14 \]

Step 4: Find the Value of x

Substitute \(y = 14\) in equation (2):

\[ x – 2(14) = 10 \]

\[ x – 28 = 10 \]

\[ x = 38 \]

Conclusion

Present age of Salim:

\[ \boxed{38 \text{ years}} \]

Present age of daughter:

\[ \boxed{14 \text{ years}} \]