The present age of a father is the sum of the ages of his three sons. ...
The present age of a father is the sum of the ages of his three sons. ...
Problem Analysis:
Let the present ages of three sons be x, y, and z. According to the given condition, the sum of their ages is equal to the present age of the father. Hence, we can write the equation as:
x + y + z = Father's present age
After ten years, the ages of the father and three sons will increase by 10. Hence, we can write the second equation as:
Father's age after 10 years = (3/4) * Sum of their ages after 10 years
Substituting the values of x, y, and z from the first equation, we get:
Father's age + 10 = (3/4) * (x + 10 + y + 10 + z + 10)
Father's age + 10 = (3/4) * (x + y + z + 30)
Father's age + 10 = (3/4) * (Father's present age + 30)
4 * (Father's age + 10) = 3 * (Father's present age + 30)
4 * Father's age + 40 = 3 * Father's present age + 90
4 * Father's age - 3 * Father's present age = 50
Father's present age = 50 / (4 - 3) = 50
Therefore, the father's present age is 50 years.
Final Answer:
The correct answer is option (a) 50 years.