Question

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

Answer 1

Answer:

Sonal age = 24 years  and  Payal age = 12 years

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.;

                          $\frac{1}{x}+\frac{1}{y} = \frac{1}{8}$

                           $\frac{y+x}{xy} =\frac{1}{8}$

                        8(y + x) = x*y

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

                         16*y + 96 = $y^{2}$ + 12*y

                          $y^{2}$ - 4*y - 96 = 0

Now using middle term splitting method;

                         $y^{2}$ - 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.

                         

Answer 2

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