Question

The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2. Find the present age of the son?​
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Answer 1

Answer:

❍ Let the present ages of father and his son be 6x years and x years respectively.

— After five years their ages;

Son's age = (x + 5) years

Father's age = (6x + 5) years

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$\underline{\bigstar\:\boldsymbol{According \;to \;the \;given \;Question :}}$

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After five years, the ratio of their ages (father's age and son's age) will become 7: 2.

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Therefore,

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$:\implies\sf \bigg(\dfrac{6x + 5}{x + 5}\bigg) = \bigg(\dfrac{7}{2}\bigg)\\\\\\:\implies\sf 2(6x + 5) = 7(x + 5) \\\\\\:\implies\sf 12x + 10 = 7x + 35\\\\\\:\implies\sf 7x - 12x = 10 - 35\\\\\\:\implies\sf -5x = -25\\\\\\:\implies\sf x = \cancel\dfrac{-25}{-5}\\\\\\:\implies\underline{\boxed{\frak{\pink{x = 5}}}}\;\bigstar$

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Hence,

Present age of son = x = 5 years.

Present age of father = 6x = 6(5) = 30 years.

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$\therefore{\underline{\textsf{Hence, \; present\;age\;of\;son\; is\;\textbf{ 5 years}.}}}$

Answer 2

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LET THE PRESENT AGE OF SON = x

AND FATHER = 6x

AFTER 5 YEARS,

the ratio will become :-

(6x+5) and (x+5) ➣ 7:2

$\frac{6x + 5}{x + 5} = \frac{7}{2} \\ \\ = 2(6x + 5) = 7(x + 5) \\ 12x + 10 = 7x + 35 \\ 12x - 7x = 35 - 10 \\ 5x = 25 \\ x = \frac{25}{5} \\ = 5$

SO, THE AGE OF SON (x) ❥ 5

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HOPE IT HELPS