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?3 years5 years7 years4 years About the author Clara

❍ 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 ⠀⠀⠀⠀⠀ [tex]\underline{\bigstar\:\boldsymbol{According \;to \;the \;given \;Question :}}[/tex] ⠀⠀⠀⠀⠀ After five years, the ratio of their ages (father’s age and son’s age) will become 7: 2. ⠀⠀⠀⠀⠀ Therefore, ⠀⠀⠀⠀⠀ [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] ⠀⠀⠀⠀⠀ Hence, Present age of son = x = 5 years. Present age of father = 6x = 6(5) = 30 years. ⠀⠀⠀⠀⠀ [tex]\therefore{\underline{\textsf{Hence, \; present\;age\;of\;son\; is\;\textbf{Option b) 5 years}.}}}[/tex] Reply

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 Reply

❍ Let the present ages of father and his son be

6xyears andxyears respectively.—Afterfiveyears their ages;(x + 5)years(6x + 5)years⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀

fiveyears, the ratio oftheir ages(father’s age and son’s age) will become7: 2.⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀

[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]

⠀⠀⠀⠀⠀

Hence,

5 years.30 years.⠀⠀⠀⠀⠀

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

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