The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is:
👴👦 Let’s solve the problem! 🤔
Let the present age of the father be F years. 📆
Let the present age of the son be S years. 📆
10 years ago, the father’s age was F – 10 years. 🕰️
10 years ago, the son’s age was S – 10 years. 🕰️
According to the problem, 10 years ago, the father’s age was thrice the son’s age. 📝
So, F – 10 = 3(S – 10)
F – 10 = 3S – 30
F = 3S – 20
Now, let’s consider the situation 10 years hence. 🔮
10 years hence, the father’s age will be F + 10 years. 🕰️
10 years hence, the son’s age will be S + 10 years. 🕰️
According to the problem, 10 years hence, the father’s age will be twice the son’s age. 📝
So, F + 10 = 2(S + 10)
F + 10 = 2S + 20
F = 2S + 10
Now we have two equations: 📝
F = 3S – 20 … (1)
F = 2S + 10 … (2)
Equating (1) and (2), we get: 🤔
3S – 20 = 2S + 10
3S – 2S = 10 + 20
S = 30
Now, substitute S = 30 in equation (1) or (2) to find F. 📝
F = 3S – 20
F = 3(30) – 20
F = 90 – 20
F = 70
So, the present age of the father is 70 years. 📆
And, the present age of the son is 30 years. 📆
The ratio of their present ages is: 📊
F : S = 70 : 30
= 7 : 3
The final answer is: 🎉 The ratio of their present ages is 7 : 3. 👴👦