Question

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

Answer 1

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

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to find out the present age of Saran and Sankar if Saran is 6 times as old as his son Sankar. Afterwards the question says that if after 4 years, he will be 4 times as old as his son. Don't be confused that who is son and who is father! Let me clear it to you! Saran is father and Sankar is son as it's given that Saran is 6 times as old as his son Sankar.

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ Saran is 6 times as old as his son Sankar.

⋆ After 4 years, he will be 4 times as old as his son.

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ The present age of Saran

⋆ The present age of Sankar

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ The present age of Saran = 36

⋆ The present age of Sankar = 6

${\bigstar \:{\pmb{\sf{\underline{Assumptions...}}}}}$

⋆ The present age of Saran is a

⋆ The present age of Sankar is b

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ As we already assumed that

⋆ The present age of Saran is a

⋆ The present age of Sankar is b

So, we have to use these assumptions to solve our question. Let us use and solve!

~ As it's already given that, Saran is 6 times as old as his son Sankar henceforth, according to this conditions be like the following:

$:\implies \sf According \: to \: the \: statement \\ \\ :\implies \sf a = 6b \dots Eq_n \: 1^{st}$

~ It is also provided to us that after 4 years, he will be 4 times as old as his son. Henceforth, according to the statement the condition be

According to the statement,

$:\implies \sf (a+4) \: = 4(b+4) \\ \\ :\implies \sf (a+4) \: = 4b + 16$

Now for solving this question we have to use equation number 1. We just have to imply its value in a. By implying we get the following:

$:\implies \sf (6b+4) \: = (4b+16) \\ \\ :\implies \sf 6b \: + 4 = \: 4b \: + 16 \\ \\ :\implies \sf 6b - \: 4b = \: 16 - 4 \\ \\ :\implies \sf 2b \: = 16 - 4 \\ \\ :\implies \sf 2b = \: 12 \\ \\ :\implies \sf b = \: \dfrac{12}{2} \\ \\ :\implies \sf b \: = 6 \\ \\ {\pmb{\sf{Therefore, \: Sankar \: is \: 6 \: years \: old}}}$

As father is 6 times old than son. Remember that a = 6b as father is 6 times old as his son Sankar. Now according to this statement,

$:\implies \sf 6b \\ \\ :\implies \sf 6(6) \\ \\ :\implies \sf 6 \times 6 \\ \\ :\implies \sf 36 \\ \\ :\implies \sf a \: = 36 \\ \\ {\pmb{\sf{Therefore, \: Saran \: is \: 36 \: years \: old}}}$