Question

Example 19: Present ages of Anu and Raj are in the ratio 4:5. Eight years from now
the ratio of their ages will be 5:6. Find their present ages
nectively​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6.

$\bf{\red{\underline{\bf{To\;find\::}}}}$

Their present ages.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the present age of Anu be 4r

Let the present age of Raj be 5r

A/q

$\underbrace{\bf{After\:8\:years\::}}}}$

The age of Anu's = 4r + 8 years

The age of Raj's = 5r + 8 years

So;

$\longrightarrow\sf{\dfrac{4r+8}{5r+8} =\dfrac{5}{6} }\\\\\\\longrightarrow\sf{6(4r+8)=5(5r+8)}\\\\\\\longrightarrow\sf{24r+48=25r+40}\\\\\\\longrightarrow\sf{24r-25r=40-48}\\\\\\\longrightarrow\sf{\cancel{-}r=\cancel{-}8}\\\\\\\longrightarrow\sf{\orange{r=8\:years}}$

Thus;

$\underbrace{\bf{The\:present\:age\:of\:Anu's=4r=(4\times 8)=\boxed{\sf{32\:years}}}}}}\\\underbrace{\bf{The\:present\:age\:of\:Raj's=5r=(5\times 8)=\boxed{\sf{40\:years}}}}}}$

Answer 2

$\huge\sf{Answer:}$

☆ Given:

⇏ Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6.

☆ Find:

⇏ Find their present ages.

☆ According to the question:

⇏ Let us assume 4x and 5x as present ages of Anu and Raj and let (4x + 8) and (5x + 8) be their ages after eight years.

☆ Calculations:

⇏ $\sf \dfrac{4x + 8}{5x + 8} = \dfrac{5}{6}$

⇏ $\sf 6 (4x + 8) = 5 (5x + 8)$

⇏ $\sf [(24x + 48) = (25x + 40)]$

⇏ $\sf [(24x - 25x) = (40 - 48)]$

⇏ ${\sf{\underline{\boxed{\green{\sf{( \cancel{-x = -8)} = (x = 8)}}}}}}$

☆ A.T.Q Let's find their present ages:

⇏ $\sf 4x = (4 \times 8)$

⇏ $\sf 5x = (5 \times 8)$

Therefore, Present age of Anu = ${\sf{\underline{\boxed{\green{\sf{32 \: years}}}}}}$ and Present age of Raj = ${\sf{\underline{\boxed{\green{\sf{40 \: years. }}}}}}$