Two years ago, Salim was thrice his daughter's age. Six years later, he will be four years older than twice her age. Find their present ages.
Salim: \(38\) years; Daughter: \(14\) years.
Step 1: Assume present ages.
Let Salim's present age be \(S\) years.
Let his daughter's present age be \(D\) years.
Step 2: Write the first condition.
Two years ago, Salim was thrice his daughter's age.
That means:
\(S - 2 = 3(D - 2)\)
Simplify:
\(S - 2 = 3D - 6\)
\(S = 3D - 4\) … (1)
Step 3: Write the second condition.
Six years later, Salim will be four years older than twice her age.
That means:
\(S + 6 = 2(D + 6) + 4\)
Simplify:
\(S + 6 = 2D + 12 + 4\)
\(S + 6 = 2D + 16\)
\(S = 2D + 10\) … (2)
Step 4: Solve the two equations.
From (1): \(S = 3D - 4\)
From (2): \(S = 2D + 10\)
Equating them:
\(3D - 4 = 2D + 10\)
\(3D - 2D = 10 + 4\)
\(D = 14\)
Step 5: Find Salim's age.
Put \(D = 14\) in (1):
\(S = 3(14) - 4\)
\(S = 42 - 4\)
\(S = 38\)
Final Answer:
Salim is 38 years old and his daughter is 14 years old.