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 s

2 thoughts on “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 s”

1. ❍ 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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   [tex]\underline{\bigstar\:\boldsymbol{According \;to \;the \;given \;Question :}}[/tex]

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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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   [tex]:\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[/tex]

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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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   [tex]\therefore{\underline{\textsf{Hence, \; present\;age\;of\;son\; is\;\textbf{Option b) 5 years}.}}}[/tex]

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2. Answer:

   F/S = 6/1

   F = 6S ….(1)

   and after 5 years

   (F+ 5)/(S+5) = 7/2

   2F + 10 = 7S + 35

   2(6S) + 10 = 7S + 35 [From (1)]

   12S + 10 = 7S + 35

   5S = 25

   S = 5 years

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