Step 1: Let the man's present age be \( m \) and the daughter's present age be \( d \). Step 2: According to the problem, the sum of their ages is \( 60 \) years, which gives us the equation \( m + d = 60 \). Step 3: Six years ago, the man's age was \( m - 6 \) and the daughter's age was \( d - 6 \). According to the problem, six years ago, the man's age was thrice that of his daughter's age, which gives us the equation \( m - 6 = 3(d - 6) \). Step 4: Simplify the second equation to find \( m \) in terms of \( d \): \[ m - 6 = 3d - 18 \] \[ m = 3d - 12 \] Step 5: Substitute \( m = 3d - 12 \) into the first equation: \[ 3d - 12 + d = 60 \] \[ 4d = 72 \] \[ d = 18 \] Step 6: Substitute \( d = 18 \) into the first equation to find \( m \): \[ m + 18 = 60 \] \[ m = 42 \] So, the man is \( 42 \) years old and the daughter is \( 18 \) years old.