Question

The ages of Anil & Sohan are in the ratio 3:8 four years from the ration of their ages
will be 1:2. Find their present age

Answer 1

Appropriate Question:

• The ages of Anil and Sohan are in the ratio of 3 : 8. Four years from now the ratio of their ages will be 1 : 2. Find their present ages.

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Given: The ages of Anil and Sohan are in the ratio 3 : 8. & Four years from now their ages will be 1 : 2.

Need to find: Their present ages?

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❍ Let's say, that the present age of Anil and Sohan be 3x and 8x respectively.

⠀

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

• It is given that, after four years the age of Anil and Shona will be in the ratio of 1 : 2.

⠀

⌑ After Four years, their ages —

• Anil's age = (3x + 4)
• Sohan's age = (8x + 4)

⠀

Now,

⠀⠀

$:\implies\sf \Bigg\{\dfrac{3x + 4}{8x + 4}\Bigg\} = \Bigg\{\dfrac{1}{2}\Bigg\}$

$:\implies\sf 2\Big\{3x + 4\Big\} = 1\Big\{8x + 4\Big\}$

$:\implies\sf 6x + 8 = 8x + 4$

$:\implies\sf 6x - 8x = 4 - 8$

$:\implies\sf -2x = -4$

$:\implies\sf x = \cancel\dfrac{-4}{-2}$

$:\implies\underline{\boxed{\pmb{\frak{\red {x = 2}}}}}\;\bigstar$

Therefore,

• Present age of Anil, 3x = 3(2) = 6
• Present age of Sohan, 8x = 8(2) = 16

$\therefore{\underline{\textsf{Hence, present age of Anil \& Sohan are \textbf{6 years} \& \textbf{16 years} respectively.}}}$

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• V E R I F I C A T I O N :

⠀

• It is Given that, after four years the age of Anil and Shona will be in the ratio of 1 : 2. So, Let's Verify the answer —

⠀

$\dashrightarrow\sf \Bigg\{\dfrac{3x + 4}{8x + 4}\Bigg\} = \Bigg\{\dfrac{1}{2}\Bigg\}$

$\dashrightarrow\sf \Bigg\{\dfrac{3(2) + 4}{8(2) + 4}\Bigg\} = \Bigg\{\dfrac{1}{2}\Bigg\}$

$\dashrightarrow\sf \dfrac{6 + 4}{16 + 4} = \dfrac{1}{2}$

$\dashrightarrow\sf \cancel\dfrac{10}{20} = \dfrac{1}{2}$

$\dashrightarrow\underline{\boxed{\pmb{\frak{\dfrac{1}{2} = \dfrac{1}{2}}}}}$

$\quad\quad\quad\;\;\therefore{\underline{\pmb{\mathcal{HENCE\; VERIFIED!}}}}$

⠀

Answer 2

Correct Question :-

• The ages of Anil & Sohan are in the ratio 3:8. Four years from now the ratio of their ages will be 1:2. Find their present ages.

Required Answer :-

• Present age of Anil is 6 years.
• Present age of Sohan is 16 years.

Explanation :-

Given :-

• Ratio of ages of Anil & Sohan = 3:8
• Four years from now ratio of their ages will be = 1:2

To Find :-

• Their present ages?

Solution :-

• Let their present ages be 3n years & 8n years.
• So, four years from now their ages will be (3n + 4) years & (8n + 4) years.

According to the question,

• Four years from now ratio of their ages will be 1:2.

Therefore,

⇒ $\sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}$

By cross multiplication,

⇒ $\sf 2(3n + 4) = 1(8n + 4)$

⇒ $\sf 6n + 8 = 8n + 4$

⇒ $\sf 8n - 6n = 8 - 4$

⇒ $\sf 2n = 4$

⇒ $\sf n = {\cancel{\dfrac{4}{2}}}$

➠ $\bf\red{n = 2}$

Hence,

↦ Present age of Anil = 3n

↦ Present age of Anil = 3 × 2

➦ Present age of Anil = 6 years

Also,

↦ Present age of Sohan = 8n

↦ Present age of Sohan = 8 × 2

➦ Present age of Sohan = 16 years

∴ Hence, present ages of Anil & Sohan are $\boxed{\bf{6\: years}}$ & $\boxed{\bf{16\: years}}$.

Let's Verify :-

We know that,

↪ $\sf \dfrac{3n + 4}{8n + 4} = \dfrac{1}{2}$

Put of n = 2 we get,

↪ $\sf \dfrac{(3\:\times\:2) + 4}{(8\:\times\:2) + 4} = \dfrac{1}{2}$

↪ $\sf \dfrac{6 + 4}{16 + 4} = \dfrac{1}{2}$

↪ $\sf {\cancel{\dfrac{10}{20}}} = \dfrac{1}{2}$

↪ $\sf \dfrac{1}{2} = \dfrac{1}{2}$

➢ $\bf \purple{LHS = RHS}$

Hence, Verified ✔

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