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 age. ​

Answer 1

Step-by-step explanation:

"Lets assume sons age = x

so , fathers age will be = 3x

Now ,

After 10 years ,

Sons age = x+10

And fathers age = 3x+10

Given that sum of their age is equal to 100 , so

( x+10) +(3x+10) = 100

x = 20

Now , Multiplying 3×x = 60

Current age of father is 60 years and son is 20 years"

Answer 2

.

Complete step-by-step 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

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

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