Question

Five years ago, Ajay was thrice as old as Sonu. Ten years later, Ajay will be twice as old as Sonu. How old are Ajay and Sonu? .Solve it by graphical method.

ig :- itzvenom6​

Answer 1

$\rm{Age \ of \ Ajay \ = \ x – 5 \ years}$

$\rm{Age \ of \ Sonu \ = y – 5 \ years}$

$\rm{Ajay \ was \ thrice \ as \ old \ as \ Sonu}$

$\implies\rm{x - 5 = 3(y – 5)}$

$\implies\rm{x - 5 = 35 – 15}$

$\implies\rm{x – 3y = -15 + 5}$

$\implies\rm{x – 3 y = - 10 ... (1)}$

$\underline{\rm{Ten \ years \ later}}$

$\rm{Age \ of \ Ajay = x + 10}$

$\rm{Age \ of \ Sonu = y + 10}$

$\rm{Ajay \ will \ be \ twice \ as \ old \ as \ Sonu}$

$\implies\rm{x + 10 = 2(y+10)}$

$\implies\rm{x + 10 = 2y + 20}$

$\implies\rm{x – 2y = 10 ... (2)}$

$\implies\rm{x – 3 y = - 10 ... (3)}$

$\underline{\rm{Subtracting \ equation \ (1) \ from \ equation \ (2)}}$

$\underline{\rm{we \ get}}$

$\fbox{\rm{y = 20}}$

$\rm{Plug \ this \ value \ in \ equation \ first \ we \ get}$

$\implies\rm{x - 3 × 20 = -10}$

$\implies\rm{x = 60 - 10}$

$\implies\rm{x = 50}$

$\rm{Hence \ age \ of \ Ajay = 50yrs}$

$\rm{and \ age \ of \ Sonu = 20yrs}$

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