Question

The present age of rams mother is three times the present age of ram. after 5 years their ages will add to 66 years . Find their present ages.​

Answer 1

Answer:

Raman's age = 14

Raman's mother's are = 42

Step-by-step explanation:

let Raman's age =x

Raman's mother's age =3x

after 5 years, their ages are x+5 and 3x+5

=> x+5+3x+5=66(given)

=> 4x +10=66

=> 4x=66-10

=> 4x=56

=> x=56/4

=> x=14

therefore,

Raman's age = x = 14

Raman's mother's age = 3x = 3*14 = 42

Answer 2

Given that,

• the present age of ram's mother is three times the present age of ram. After five years, their ages will add to 66 years.

❍ Let's say, that the present age of Ram be M years and present age of Ram's mother be N years.

$\begin{gathered}\underline{\bigstar\:{\pmb{\boldsymbol{According\;to\;the\; Question\; :}}}}\\\\\end{gathered}$

⠀

• The present age of ram's mother is three times the present age of ram.

⠀

$\begin{gathered}\longrightarrow\sf Mother = 3\times Ram\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf N = 3M\qquad\qquad\quad\sf\bigg\lgroup eq^{n}\;(1)\bigg\rgroup\\\\\end{gathered}$

▪︎ From the given second condition —

⠀

• After five years, their ages (Mother's age and son's age) will add to 66 years.

⠀

☆ After Five years, their ages —

• Ram's age = (M + 5)
• Mother's age = (N + 5)

⠀

$\begin{gathered}\longrightarrow\sf M + 5 + N + 5 = 66\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M + N + 10 = 66\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M + N = 66 - 10\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M + N = 56\qquad\qquad\quad\sf\bigg\lgroup eq^{n}\;(2)\bigg\rgroup\\\\\end{gathered}$

✇ Substituting the value 'N' from eqⁿ ( 1 ) in eqⁿ ( 2 ) —

⠀

$\begin{gathered}\longrightarrow\sf M + N = 56 \\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M + 3M = 56\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf 4M = 56 \\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M = \cancel\dfrac{56}{4}\\\\\end{gathered}$

$\begin{gathered}\longrightarrow{\pmb{\sf{\purple{M = 14}}}}\\\\\end{gathered}$

⠀⠀

» Substituting the value of 'M' in eqⁿ ( 1 ) —

⠀

$\begin{gathered}\longrightarrow\sf N = 3M\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf N = 3(14)\\\\\end{gathered}$

$\begin{gathered}\longrightarrow{\pmb{\sf{\purple{N = 42}}}}\\\\\end{gathered}$

∴ Therefore, the present age of Ram's Mother is 42 years and present age of Ram is 14 years.