Question

The difference between the ages of a mother and her daughter is 24 year. The sum of the reciprocals of their ages is 1/9 .Complete the following .​

Answer 1

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Answer 2

SOLUTION

GIVEN

The difference between the ages of a mother and her daughter is 24 year. The sum of the reciprocals of their ages is 1/9

TO DETERMINE

The ages of mother and daughter

EVALUATION

Let the age of mother = x and the age of daughter = x - 24

So by the given condition

$\displaystyle \sf{ \frac{1}{x} + \frac{1}{x - 24} = \frac{1}{9} }$

$\displaystyle \sf{ \implies \frac{x + x - 24 }{x(x - 24)} = \frac{1}{9} }$

$\displaystyle \sf{ \implies \frac{2 x - 24 }{ {x}^{2} - 24x } = \frac{1}{9} }$

$\displaystyle \sf{ \implies {x}^{2} - 24x = 18x - 216 }$

$\displaystyle \sf{ \implies {x}^{2} -42x + 216 = 0 }$

$\displaystyle \sf{ \implies {x}^{2} -36x - 6x+ 216 = 0 }$

$\displaystyle \sf{ \implies (x - 36)(x - 6) = 0 }$

$\displaystyle \sf{ \implies x = 36 \: ,\: 6 }$

x ≠ 6

Since if x = 6 then age of mother is 6 years and age of daughter is - 18 years - - - which is absurd

∴ x = 36

Hence age of mother = 36 years and age of daughter = 12 years

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