Question

3. Them age of A is five years more than that of B.5 years ago, the ratio of their age was 3:2. Find their present ages​

Answer 1

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{red}{\rm{Question}}}}}$

Them age of A is five years more than that of B.5 years ago, the ratio of their age was 3:2. Find their present ages.

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\underline{\color{green}{\rm{Required\:Answer}}}}}$

${\large{\color{blue}{\sf{Present\:age\:of\:B=15\:years}}}}$

${\large{\color{blue}{\sf{Present\:age\:of\:A=x+15=15+5=20\:years}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\underline{\underline{\rm{Given}}}}}$

${\sf{A\:is\:five\:years\:more\:than\:b}}$

${\sf{Given\:Ratio=3:2}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\qquad{\qquad{\qquad{\large{\sf{Let\:age\:of\:b=x\:years}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{5\:years\:ago:}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{A's\:age=x\:years}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{B's\:age=x-5\:years}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{A:B=3:2}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{\frac{x}{x-5}=\frac{3}{2}}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{2x=3(x-5)}}}}}}$

${\qquad{\qquad{\qquad{\large{\sf{3x-2x=15}}}}}}$

${\qquad{\qquad{\qquad{\large{\boxed{\bigstar{\color{red}{\sf{x=15\:years}}}}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\huge{\underline{\color{green}{\rm{Answer}}}}}$

${\large{\underline{\boxed{\color{blue}{\sf{Present\:age\:of\:B=15\:years}}}}}}$

${\large{\boxed{\color{blue}{\sf{Present\:age\:of\:A=x+15=15+5=20\:years}}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Answer 2

Given data : The age of A is five years more than that of B. 5 years ago, the ratio of their age was 3:2.

To find : Find their present ages ?

Solution : Let, the age of B be x years.

A/C to given data;

➜ Age of B = x years ----{1}

➜ Age of A = (x + 5) years ----{2}

Five years ago :

➜ Age of B = (x - 5) years

➜ Age of A = {(x + 5) - 5} years = x years

Now, a/c to given data; {five years ago, ratio of thire age was 3:2}

➜ A : B = 3 : 2

➜ x/(x - 5) = 3/2

➜ 2x = 3(x - 5)

➜ 2x = 3x - 15

➜ 2x - 3x = 15

➜ - x = - 15

➜ x = 15 years

from eq. {1}

Hence, Age of B is 15 years.

Put value of x in eq. {1}

➜ Age of A = (x + 5)

➜ Age of A = (15 + 5)

➜ Age of A = 20 years

Answer : Hence, age of the A is 20 years and age of the B is 15 years.

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