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.
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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.
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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.
Verified answer
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.
[tex]\underline{\bigstar\:{\pmb{\boldsymbol{According\;to\;the\; Question\; :}}}}\\\\[/tex]⠀
⠀
[tex]\longrightarrow\sf Mother = 3\times Ram\\\\[/tex]
[tex]\longrightarrow\sf N = 3M\qquad\qquad\quad\sf\bigg\lgroup eq^{n}\;(1)\bigg\rgroup\\\\[/tex]
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
▪︎ From the given second condition —
⠀
⠀
☆ After Five years, their ages —
⠀
[tex]\longrightarrow\sf M + 5 + N + 5 = 66\\\\[/tex]
[tex]\longrightarrow\sf M + N + 10 = 66\\\\[/tex]
[tex]\longrightarrow\sf M + N = 66 - 10\\\\[/tex]
[tex]\longrightarrow\sf M + N = 56\qquad\qquad\quad\sf\bigg\lgroup eq^{n}\;(2)\bigg\rgroup\\\\[/tex]
✇ Substituting the value 'N' from eqⁿ ( 1 ) in eqⁿ ( 2 ) —
⠀
[tex]\longrightarrow\sf M + N = 56 \\\\[/tex]
[tex]\longrightarrow\sf M + 3M = 56\\\\[/tex]
[tex]\longrightarrow\sf 4M = 56 \\\\[/tex]
[tex]\longrightarrow\sf M = \cancel\dfrac{56}{4}\\\\[/tex]
[tex]\longrightarrow{\pmb{\sf{\purple{M = 14}}}}\\\\[/tex]
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀
» Substituting the value of 'M' in eqⁿ ( 1 ) —
⠀
[tex]\longrightarrow\sf N = 3M\\\\[/tex]
[tex]\longrightarrow\sf N = 3(14)\\\\[/tex]
[tex]\longrightarrow{\pmb{\sf{\purple{N = 42}}}}\\\\[/tex]
∴ Therefore, the present age of Ram's Mother is 42 years and present age of Ram is 14 years.