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:

Let present age of ram is X

so present age of ram's mother = 3X

After 5 years, ram's age = X+5

After 5 years ram's mother's age = 3X+ 5

Also sum of both age after 5 years = 66

so, X+5 + 3X+5 = 66

4X+ 10 = 66

4X = 56

X = 56/4

X= 14

HENCE, RAM'S AGE IS 14 YEARS.

RAM'S MOTHER'S AGE = 3* 14 = 52 YEARS.

Therefore, ram's present age is 14 years. His mother's present age is 52 years.

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.

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

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

⠀

$\longrightarrow\sf Mother = 3\times Ram$

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

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

▪︎ 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)

⠀

$\longrightarrow\sf M + 5 + N + 5 = 66$

$\longrightarrow\sf M + N + 10 = 66$

$\longrightarrow\sf M + N = 66 - 10$

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

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

⠀

$\longrightarrow\sf M + N = 56$

$\longrightarrow\sf M + 3M = 56$

$\longrightarrow\sf 4M = 56$

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

$\longrightarrow{\pmb{\sf{\purple{M = 14}}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

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

⠀

$\longrightarrow\sf N = 3M$

$\longrightarrow\sf N = 3(14)$

$\longrightarrow{\pmb{\sf{\purple{N = 42}}}}$

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