Question

The difference between age of a mother and her daughter is 24 .The sum of the reciprocal of their ages is 1/9 .Find the mother age

Answer 1

her mother age is 36 yrs

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Answer 2

Step-by-step explanation:

Given that

Difference between age of a mother and her daughter is 24.

Sum of the reciprocal of their ages is 1/9

To find

Mother age

Solution

Let the age of the mother be x and the age of the daughter be y . Since the difference between their ages is 24, we have

$x - y = 24 \\ \times = 24 + y$

then as per 2nd given condition

$\frac{1}{x} + \frac{1}{y} = \frac{1}{9}$

by doing cross multiplications we get

$9(y + x) = xy$

put 1st equation in this

$9(y + (24 + y)) = (24 + y) \times y$

by solving this we get equation as

${y}^{2} + 6y - 216 = 0$

by taking its square roots we get

$(y + 18)(y - 12) = 0$

hence

$y = - 18 \: \: \: \: \: y = 12$

negative value we can not take hence y is 12year.

put value of y in equation 1

we get

$x = 24 + 12$

$x = 36year$

hence Age of mother is 36year.