Question

4 years ago ramus age is square root ofhis father age. now the age of ramu and his father is in ratio 1:4 then what is ramus age??​

Answer 1

4 years ago, Ramu's age was square root of his father's age. Let us assume Ramu's age as x. So obviously, his father's age is x².

Now, their ages are in the ratio 1:4, that is, after 4 years.

Their ages now will be

Ramu = (x + 4) years.

Father = (x² + 4) years.

Ratio = 1:4

Hence,

$\frac{x+4}{x^2+4}=\frac{1}{4}$

$4(x+4) = x^2+4$

$4x + 16 = x^2+4$

$x^2-4x-12 = 0$

$x^2 - 6x + 2x -12 =0$

$x(x-6) +2(x-6) = 0$

$(x+2)(x-6) = 0$

x = -2  OR  x = 6

Since age can't be negative,

Ramu's age 4 years ago was 6. His fathers age was 36.

Now Ramu's age is 10 and that of his father is 40.