Question

four years ago, anju was three times as old as her son. Six years from now Mother will be 1 year older than twice the age of her son. Find their ages​

Answer 1

AnswEr :

Let's say that , Present age of Anju be M years & Present age of her Son be N years .

» Before 4 Year their ages :

• Anju age will be : ( M - 4 ) years &
• Anju's son age will be : ( N - 4 ) years .

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⠀(I) Four Years ago , Anju was three times as old as her Son .

$\\:\implies \sf Anju \:=\: 3 \times Son \:$

$:\implies \sf ( \:M \; - 4 \:) \:=\: 3 \times (\:N - 4\:) \:$

$:\implies \sf ( \:M \; - 4 \:) \:=\: (\:3N - 12\:) \:$

$:\implies \sf \:M \; - 4 \:=\: 3N - 12 \:$

$:\implies \sf \:M \; - 3N \:=\: - 8 \:\:\qquad \bigg\lgroup \:Eq^n\:(1)\:\bigg\rgroup \:$

» After 6 Year their ages :

• Anju age will be : ( M + 6 ) years &
• Anju's son age will be : ( N + 6 ) years .

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⠀(II) Six years from now Anju's age will be 1 year older than twice the age of her son .

$\\\longrightarrow \sf Anju = \; 2\:(\:Son \:)\:+\:1\:$

$\longrightarrow \sf (\: M + 6\:) = \; 2\:(\:N + 6 \:)\:+\:1\:$

$\longrightarrow \sf (\: M + 6\:) = \; \:(\:2N + 12 \:)\:+\:1\:$

$\longrightarrow \sf \: M + 6\: =\:2N + 13 \:$

$\longrightarrow \sf \: M\: =\:2N + 13 - 6 \:$

$\longrightarrow \sf \: M\: =\:2N + 7 \:\:\:\qquad \bigg\lgroup \:Eq^n\:(2)\:\bigg\rgroup$

$\qquad \dag\:\underline {\sf Substituting \:Eq^n(2)\:in \:Eq^n\:(1)\::\:}$

$\longrightarrow \sf M - 3N\:=\:-8\:$

$\longrightarrow \sf ( 2N + 7 ) - 3N\:=\:-8\:$

$\longrightarrow \sf 2N - 3N\:=\:-8\:-\:7\:$

$\longrightarrow \sf -N\:=\:-15\:$

$\longrightarrow \pmb{\sf N\:=\:15\:}\:$

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✇ Substituting , the Value of 'N' in Eq.(2) we get —

$\\\dashrightarrow \sf \: M\: =\:2N + 7 \:$

$\dashrightarrow \sf \: M\: =\:2(15) + 7 \:$

$\dashrightarrow \sf \: M\: =\:30 + 7 \:$

$\dashrightarrow \pmb{\sf M\:=\:37\:}\:$

Therefore ,

• Present age of Anju is , M = 37 years &
• Present age of Anju's son is , N = 15 year .

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∴ Hence , Present ages of Anju and her Son are 37 years and 15 year , respectively.

Answer 2

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