Question

two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. find their present ages​

Answer 1

AnswEr :

Let the Present Age of Father be x yrs, and Present Age of Son be y yrs.

• 2⠀Y E A R S⠀A G O (Past) :

◗ Father = Present – 2 = (x – 2) yrs

◗ Son = Present – 2 = (y – 2) yrs

• According to the Question :

↠ Father = Three times of Son

↠ (x – 2) = 3 × (y – 2)

↠ x – 2 = 3y – 6

↠ x = 3y – 6 + 2

↠ x = 3y – 4 ⠀⠀⠀⠀⠀⠀—eq.( I )

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• 2⠀Y E A R S⠀H E N C E (Future) :

◗ Father = Present + 2 = (x + 2) yrs

◗ Son = Present + 2 = (y + 2) yrs

• According to the Question Now :

↠ Twice of Father = Five times of Son

↠ 2 × (x + 2) = 5 × (y + 2)

• Putting the value of x from eq.( I )

↠ 2 × (3y – 4 + 2) = 5 × (y + 2)

↠ 2 × (3y – 2) = 5 × (y + 2)

↠ 6y – 4 = 5y + 10

↠ 6y – 5y = 10 + 4

↠ y = 14 yrs

• Putting value of y in eq.( I ) :

↠ x = 3y – 4

↠ x = 3(14) – 4

↠ x = 42 – 4

↠ x = 38 yrs

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• P R E S E N T⠀A G E S :

◗ Father = x = 38 Years

◗ Son = y = 14 Years

∴ Present Age of Father and Son will be 38 Years and 14 Years respectively.

Answer 2

$\huge\underline{\fcolorbox{black}{white}{Answer}}$

$Let,\\ \: the \: present \: age \: of \: son \: be \: x \\ \: the \: present \: age \: of \: father \: be \: y \\ \\ \:<strong><u>Now</u></strong><strong><u>,</u></strong>\\ 2 \: years \: ago \: sons \: age \: was \:( x - 2)yrs \\ 2 \: years \: ago \: fathers \: age \: was \: (y - 2)yrs \\ \\ Again,\\ 2 \: years \: hence \: sons \: age \: will \: be \: (x + 2)yrs \\ 2 \: years \: hence \: fathers \: age \: will \: be \: (x + 2)yrs \\ \\ A/Q\\ 3(x - 2) = y - 2 \: ......... \: \: eq(1)\\ And,\\ 5(x + 2) = 2(y + 2) \: .......... \: \: eq(2) \\ \\ From \: eq(1) \\ 3x - 6 = y - 2 \\ = > 3x - y = - 2 + 6 \\ = > 3x - y = 4 \: ......... \: \: eq(3) \\ \\ From \: eq(2) \\ 5x + 10 = 2y + 4 \\ = > 5x - 2y = 4 - 10 \\ = > 5x - 2y = - 6 \: .......... \: \: eq(4) \\ \\ Now, \\ eq(3) \times 2 = 6x - 2y = 8 \: ..... \: \: eq(5)\\ eq(4) \times 1 = 5x - 2y = -6..... \: \: eq(6) \\ \\ eq.(5) - eq(6) \\ 6x - 5x - 2y + 2y = 8 + 6 \\ = > x = 14 \\ \\ Putting \: x = 14 \: in \: eq(3) \\ 3x - y = 4 \\ = > 3 \times 14 - y = 4 \\ = > 42 - y = 4 \\ = > y = 42 - 4 \\ = > y = 38 \\ \\ So,\: \\ present \: age \: of \: father \: is \: 38 \: years \\ present \: age \: of \: son \: is \: 14 \: years$

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