Question

The present age of a son is half the present age of his father. Ten years ago, the father was thrice as old as his son. What are their present ages?

Answer 1

Let the present age of the son and the father be ‘S’ and ‘F’ respectively.

According to the question, the present age of the son is half the present age of his father. So, we can write

S=12×F−−−−(i)S=12×F−−−−(i)

Now, ten years ago, the ages of the son and the father were given as

Son’s age = (S-10) years and Father’s age = (F-10) years

Also, it is given in the question that ten years ago, the father was thrice as old as his son. So, we can write

F−10=3(S−10)⇒F−10=3S−30⇒3S−F=30−10⇒3S−F=20−−−−(ii)F−10=3(S−10)⇒F−10=3S−30⇒3S−F=30−10⇒3S−F=20−−−−(ii)

Now, solving the equations (i) and (ii) for the present ages of the father and son.

Substituting the value from the equation (i) in the equation (ii), we get

⇒3S−F=20⇒3(12×F)−F=20⇒12×F=20⇒3S−F=20⇒3(12×F)−F=20⇒12×F=20

On cross-multiplying the terms, we get

⇒12×F=20F=40⇒12×F=20F=40

Hence, the present age of the father is 40 years.

Now, again substituting the value of the present age of father in the equation (i) to determine the present age of the son.

S=12×F=12×40=20S=12×F=12×40=20

Hence, the present age of the son is 20 years.

Answer 2

Answer:

Let the present age of the son and the father be ‘S’ and ‘F’ respectively.

According to the question, the present age of the son is half the present age of his father. So, we can write

S=12×F−−−−(i)

Now, ten years ago, the ages of the son and the father were given as

Son’s age = (S-10) years and Father’s age = (F-10) years

Also, it is given in the question that ten years ago, the father was thrice as old as his son. So, we can write

F−10=3(S−10)⇒F−10=3S−30⇒3S−F=30−10⇒3S−F=20−−−−(ii)

Now, solving the equations (i) and (ii) for the present ages of the father and son.

Substituting the value from the equation (i) in the equation (ii), we get

⇒3S−F=20⇒3(12×F)−F=20⇒12×F=20

On cross-multiplying the terms, we get

⇒12×F=20F=40

Hence, the present age of the father is 40 years.

Now, again substituting the value of the present age of father in the equation (i) to determine the present age of the son.

S=12×F=12×40=20