Question

Five years later, the Jacob age will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?
A. Jacob = 80 years, son = 40 years.
B. Jacob = 30 years, son = 10 years.
C. Jacob = 40 years, son = 10 years.
D. Jacob = 50 years, son = 20 years.

Answer 1

Hint – In order to solve this problem you need to assume the variables for the present age of Jacob and his son then make equations according to question and solve the problem.

Complete step-by-step answer:
Let the present age of Jacob be x and that of his son be y.
It is given that five years later, the Jacob age will be three times that of his son.
Jacob age 5 years later will be x+5 and that of his son will be y+5.
So we do, x + 5 = 3(y+5)
x - 10 = 3y ……(1)
It is also given that five years ago, Jacob age was seven times that of his son.
Jacob age 5 years ago will be x-5 and that of his son will be y-5.
So we do, x – 5 = 7(y-5)
x + 30 = 7y ……(2)
Subtracting equation (1) from (2) we get,
40=4y
So, we get y = 10
On putting the value of y in equation (1) we get,
x – 10 = 3(10)
x = 30+10=40
x = 40
Hence, the present age of Jacob is 40 and that of his son is 10.
The right option is C.

Note – In these types of problems you need to assume variables according to the question provided then solve. Remember to make the number of equations equal to the number of variables. Also remember if you are writing the age of 5 years later then everybody’s present age will be written in 5 years later same for the ages ago. Proceeding like this will give you the right answer.