Question

The ages of Ramesh and Rahim are in the ratio of 5:7 if ramesh was 9 years older and rahim was 9 years younger the age of ramesh would have been twice the age of rahim. Find their ages.

Answer 1

Answer :

Present age of Ramesh is 15 years and present age of Rahim is 21 years.

Given :

• The ages of Ramesh and Rahim are in the ratio of 5:7.
• If Ramesh was 9 years older and Rahim was 9 years younger , the age of Ramesh would have been twice the age of Rahim.

To find :

• Their ages.

Solution :

Consider,

• Age of Ramesh = 5x
• Age of Rahim = 7x

If Ramesh was 9 years older and Rahim was 9 years younger, the age of Ramesh would have been twice the age of Rahim.

• Ramesh = (5x+9) years
• Rahim = (7x-9) years

According to the question :-

$\to\sf{5x+9=2(7x-9)}$

$\to\sf{5x+9=14x-18}$

$\to\sf{5x-14x=-18-9}$

$\to\sf{9x=27}$

$\to\sf{x=3}$

★ Present age of Ramesh = 5×3 = 15 years

★ Present age of Rahim = 7×3 = 21 years

Answer 2

★ Given : The ages of Ramesh and Rahim are in the ratio of 5:7 if ramesh was 9 years older and rahim was 9 years younger the age of ramesh would have been twice the age of rahim.

$\rule{130}1$

★ Solution :

$\begin{lgathered}\bullet\:\:\textsf{Let age of Ramesh be \textbf{5x}}\\\bullet\:\:\textsf{and age of Rahim be \textbf{7x}}\end{lgathered}$

$\begin{lgathered}\bullet\:\:\textsf{Ramesh 9 years older will be \textbf{5x + 9 years}}\\\bullet\:\:\textsf{Rahim 9 years younger will be \textbf{7x - 9 years}}\end{lgathered}$

$\rule{130}1$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\begin{lgathered}:\implies\sf 2(7x - 9) = 5x + 9\\\\\\:\implies\sf 14x - 18 = 5x + 9\\\\\\:\implies\sf 14x - 5x = 9 + 18\\\\\\:\implies\sf 9x = 27\\\\\\:\implies\sf x = \dfrac{27}{9} \\\\\\:\implies\sf x = 3\end{lgathered}$

$\rule{170}2$

☯ $\underline{\boldsymbol{The\: Age\:of\: Ramesh\:\&\:Rahim:}}$

$\begin{lgathered}\bullet\:\:\textsf{Rahim = 5x = 5(3) = \textbf{15 years}}\\\bullet\:\:\textsf{Rahim = 7x = 7(3) = \textbf{21 years}}\end{lgathered}$

$\rule{170}2$