Question

The age of a mother is 4 years less than the square of the age of the daughter. Four years later, their ages would be in the ratio of 18: 5. Find the present age of the daughter.​

Answer 1

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The age of a mother is 4 years less than the square of the age of the daughter. Four years later, their ages would be in the ratio of 18: 5. Find the present age of the daughter.

$\LARGE{\color{pink}{\textsf{\textbf{⠀solution⠀}}}}$

let the age of daughter be x

A.T.Q. :-

y = x² - 4

4 Years later :-

age of mother = ( x² - 4 ) + 4 = x²

age of daughter = x + 4

$\frac{ {x}^{2} }{x + 4} = \frac{18}{5}$

by cross multiplication:-

5x² = 18(x+4)

5x² = 18x + 72

=> 5x² - 18x - 72 = 0

factorizing the equation:-

5x² - 30x + 12x - 72

5x ( x - 6 ) + 12 ( x - 6 )

(x-6) (5x+12)

x-6 = 0

x = 6

hence, the age of daughter is 6 years !

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Hope it helps ♡

~ hαppч lєαrníng ~

Answer 2

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let the age of daughter be x

A.T.Q. :-

y = x² - 4

4 Years later :-

age of mother = ( x² - 4 ) + 4 = x²

age of daughter = x + 4

\frac{ {x}^{2} }{x + 4} = \frac{18}{5}x+4x2=518

by cross multiplication:-

5x² = 18(x+4)

5x² = 18x + 72

=> 5x² - 18x - 72 = 0

factorizing the equation:-

5x² - 30x + 12x - 72

5x ( x - 6 ) + 12 ( x - 6 )

(x-6) (5x+12)

x-6 = 0

x = 6

hence, the age of daughter is 6 years !