five years ago a man was old as his son, five years hence the father will be three times old as his son. Find their present ages.<

2 thoughts on “five years ago a man was old as his son, five years hence the father will be three times old as his son. Find their present ages.<”

1. Answer:

   Let Five years ago the age of son be x years and age of father be 7x years

   Present age of son =x+5

   Present age of father =7x+5

   5 years later their age will (x+10) and (7x+10)

   ∴7x+10=3(x+10)

   7x−3x=20

   4x=20

   x=5

   So, the present age of son=x+5=5+5=10years

   and the present age of father=7x+5=35+5=40years

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2. ➲CORRECT QUESTION :

   • Five years ago, a man was seven times as old as his son. Five years hence, the father will be three times as old as his son . Find their present ages.

   ☯GIVEN :

   • Five years ago, the man was seven times as old as his son.

   • Five years hence, the father will be three times as old as his son.

   ☯TO FIND :

   • The present age of Father.

   • The present age of his son.

   ➲SOLUTION :

   ✞ Let the present age of father and his son be a years and b years.

   According to the First Condition :

   • Five years ago , the man was seven times as old as his son.

   Five years ago,

   • Age of father = (a-5) years

   • Age of his son = (b-5) years

   [tex] \implies{\sf{a-5=7(b-5)}} \\ \\[/tex]

   [tex]\implies{\sf{a-5=7b-35}} \\ \\ [/tex]

   [tex]\implies{\sf{a=7b-35+5}} \\ \\ [/tex]

   [tex]\implies\bf{a=7b-30….(i)}[/tex]

   According to the Second Condition :

   • 5 years hence, the father will be 3 times as old as his son .

   Five years hence ,

   • Age of father = (a+5) years

   • Age of son = (b+5) years

   [tex]\implies\sf{a+5=3(b+5)} \\ [/tex]

   [tex]\implies\sf{a+5=3b+15}[/tex]

   • Substituting the value of eq(1) :

   [tex]\implies\sf{7b-30+5=3b+15}\\ \\ [/tex]

   [tex]\implies\sf{7b-25=3b+15}\\ \\ [/tex]

   [tex]\implies\sf{7b-3b=15+25}\\ \\[/tex]

   [tex]\implies\sf{4b=40}\\ \\[/tex]

   [tex]\implies\sf{b=\dfrac{40}{4}}\\ \\[/tex]

   [tex]\implies \underline{\boxed{\bf{\red{b=10}}}}[/tex]

   • Substituting the value of b in eq(1) :

   [tex]\implies\sf{a=7b-30}\\ \\[/tex]

   [tex]\implies\sf{a=7\times10-30}\\ \\[/tex]

   [tex]\implies\sf{a=70-30}\\ \\[/tex]

   [tex]\implies\underline{\boxed{\bf{\red{a=40}}}}[/tex]

   [tex] \huge{ \pink{ \therefore}}[/tex] Present age of father = 40 years

   [tex] \huge{ \red{ \therefore}}[/tex]Present age of his son = 10 years

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