The difference between payal and sonal age is 12years. The sum of there reciprocals is 1/8.find there ages (sonal is elder to payal

Step-by-step explanation:

let the age of Payal be equal to "P"

and the age of Sonal be equal to "S"

Now, according to the question, S-P = 12

and

Now, S = P + 12 and putting this value of S in the above equation, we get

⇒

Solving this, we get P = 12

and therefore S = 24.

Step-by-step explanation:

Let sonal age be x years and payal age be y years.

First condition we are given that the difference between payal and sonal age is 12 years i.e.;

                       x - y = 12

                         x = y + 12 ---------- [Equation 1]

Second condition we are given that the sum of their reciprocals is 1/8, i.e.;

                        8(y + x) = x*y

                        8(y + y + 12) = y*(y + 12) {putting value of x from equation 1}

                         16*y + 96 = + 12*y

                          - 4*y - 96 = 0

Now using middle term splitting method;

                          - 12*y + 8*y - 96 = 0

                         y(y - 12) + 8(y - 12) = 0

                         (y - 12) * (y + 8) = 0

So, either y - 12 = 0  or   y + 8 = 0 i.e. either y = 12  or  y = -8.

Since age can't be negative so y = 12.

Putting value of y in equation 1 we get, x = 12 + 12 = 24.

Therefore, Sonal age, x = 24 years and Payal age, y = 12 years.