Question

At present, Aniket is twice as old as his son. If four years, he will be four times as old as what his son was 9 year ago. Find the present ages of both of them.​

Answer 1

☯ Let Present age of son be x years.

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Then, The Present age of aniket will be 2x years.

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Their ages in four years,

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• Age of aniket = 4(x - 9) years
• Age of son = 2x + 4 years

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$\dashrightarrow \large{\sf 2x = x(eq \: \: 1....)}$

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Therefore,

$\dashrightarrow \sf 2x + 4 = 4 (x - 9)$

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$\dashrightarrow \sf2x + 4 = 4x - 36$

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$\dashrightarrow \sf2x = 4x - 40$

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Then, As per equation 1,

• Two times son is equal to father(aniket).

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$\dashrightarrow \sf4x - 40 = 2x$

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$\dashrightarrow \sf4x - 2x = 40$

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$\dashrightarrow \sf2x = 40$

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$\dashrightarrow \sf x = 20$

Hence,

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• The Present age of aniket, 2x = 2 × 20 = 40 years
• And, The Present age of his son, x = 20 years

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$\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\: Verification\:\bigstar}}}} \\ \\\end{gathered}$

Given that,

• In four years, he will be four times as old as what his son was 9 years ago.

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$\begin{gathered}:\implies\sf (2x + 4) = 4(x- 9)\\ \\ \\ :\implies\sf (2(20) + 4) = 4(20- 9)\\ \\ \\:\implies\sf (40 + 4) =80 - 36\\ \\ \\:\implies\sf44 = 44\\ \\\end{gathered}$

$\qquad\qquad\qquad\quad\dag\:{\underline{\underline{\sf{\purple{Hence\: Verified!}}}}}$

Answer 2

Your answer is in attachment.