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

Step-by-step explanation:

Given :-

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

To find :-

Find their present ages ?

Solution :-

Given that :

The ratio of the present ages of Anil and Sohan = 3:8

Let they be 3X and 8X respectively.

The present age of Anil = 3X years

The present age of Sohan = 8X years

After 4 years,

The age of Anil = (3X+4) years

The age of Sohan = (8X+4) years

The ratio of the ages of Anil and Sohan after

4 years = (3X+4) : (8X+4)

According to the given problem

The ratio of their ages after 4 years = 1:2

=> (3X+4) : (8X+4) = 1:2

=> (3X+4) / (8X+4) = 1 / 2

On applying cross multiplication then

=> (8x+4)×1 = (3X+4)×2

=> 8X+4 = 6X+8

=> 8X-6X = 8-4

=> 2X = 4

=> X = 4/2

=> X = 2

Therefore, X = 2 years

The Present age of Anil = 3X years

=> 3×2 = 6 years

The present age of Sohan = 8X years

=> 8×2 = 16 years

Answer:-

The present age of Anil = 6 years

The present age of Sohan = 16 years

Check:-

The present age of Anil = 6 years

The present age of Sohan = 16 years

Ratio = 6:16 = 3:8

and

After 4 years their ages will be 6+4 = 10 years and 16+4 = 20 years

Ratio = 10:20 = 1:2

Verified the given relations in the given problem.

Answer 2

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.

Given: 

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

To find: 

• Their present ages?

Solution:⠀⠀⠀

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

$\begin{gathered} \boxed{\textsf{\blue{According\;to\;the\; Question:}}}\end{gathered}$

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

⌑ After Four years, their ages —

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

⠀

Now,

$\begin{gathered}:\implies\sf \Bigg\{\dfrac{3x + 4}{8x + 4}\Bigg\} = \Bigg\{\dfrac{1}{2}\Bigg\}\\\\\\\end{gathered} \\ \begin{gathered}:\implies\sf 2\Big\{3x + 4\Big\} = 1\Big\{8x + 4\Big\}\\\\\\\end{gathered} \\ \begin{gathered}:\implies\sf 6x + 8 = 8x + 4\\\\\\\end{gathered} \\ \begin{gathered}:\implies\sf 6x - 8x = 4 - 8\\\\\\\end{gathered} \\ \begin{gathered}:\implies\sf -2x = -4\\\\\\\end{gathered} \\ \begin{gathered}:\implies\sf x = \cancel\dfrac{-4}{-2}\\\\\\\end{gathered} \\ \begin{gathered}:\implies\underline{\boxed{\frak{x = 2}}}\pink\bigstar\\\\\end{gathered}$

Therefore,

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

$\begin{gathered}\therefore{\underline{\textsf{Hence, present age of Anil \& Sohan are \textbf{6 years} \& \textbf{16 years} respectively.}}}\\\end{gathered}</p><p>$

Thank you!

@itzshivani