1.

Saran is 6 times as old as his son Sankar. After 4 years, he will be 4 times as old ashis son. What are their present ages?​

Answer»

❍ Let's SAY, that the PRESENT AGE of Saran be x years and present age of his son Sankar be y years respectively.

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\underline{\bigstar\:\boldsymbol{According\:to\;the\; question :}}⠀

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\underline{\ \sf{Case} \: \it1 :}

  • Saran is 6 TIMES as old as his son Sankar. Saran's present age = x and Sankar present age = y years.

Therefore,

\dashrightarrow\sf( Saran's \: age ) = 6 \times ( Sankar's \: age) \\\\\\\dashrightarrow\sf x = 6 \times y \\\\\\\dashrightarrow\sf x = 6y \qquad\qquad\bigg\lgroup\sf eq^n \; 1\bigg\rgroup

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\underline{\ \sf{Case} \: \it2:}

  • After four years, he'll be four times as old as his son Sankar.

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Therefore,

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\dashrightarrow\sf \Big(x + 4\Big) = 4 \times \Big(y + 4\Big) \\\\\\\dashrightarrow\sf x + 4 = 4y + 16 \\\\\\\dashrightarrow\sf 6y + 4 = 4y + 16\qquad\qquad\bigg\lgroup\sf From~eq^n \; 1\bigg\rgroup\\\\\\\dashrightarrow\sf 6y - 4y = 16 - 4\\\\\\\dashrightarrow\sf 2y = 12\\\\\\\dashrightarrow\sf y = \cancel\dfrac{12}{2}\\\\\\\dashrightarrow\underline{\boxed{\frak{\pmb{\pink{y = 6}}}}}\;\bigstar

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⠀⠀⠀ ⠀\underline{\bf{\dag} \:\mathfrak{Putting\;value\;of\:y\;in\;eq^n \;(1)\: :}}⠀⠀⠀⠀

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\dashrightarrow\sf x = 6 \times y\\\\\\\dashrightarrow\sf x = 6 \times 6\\\\\\\dashrightarrow\underline{\boxed{\frak{\pmb{\pink{x = 36}}}}}\;\bigstar

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\therefore{\underline{\textsf{Hence, their present ages are \textbf{6 years}\:\sf{and}\;\textbf{36 years}\;{respectively}.}}}⠀⠀⠀⠀⠀⠀


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