The ages of Ramesh and Rahim are in ratio 5:7. If Ramesh was 9 years older and Rahim 9 years younger, the age of Ramesh would have been twice the age of Rahim. Find their ages.
Last updated date: 16th Mar 2023
•
Total views: 305.7k
•
Views today: 3.85k
Answer
305.7k+ views
Hint: We need to have a clear understanding of the given question to proceed further. According to the question statement, try to form an equation and proceed further.
Let the present age of Ramesh be $x$ and the present age of Rahim be $y$.
It is given that the ratio of ages of Ramesh and Rahim =5:7
$ \Rightarrow \frac{x}{y} = \frac{5}{7}$ .... (1)
It is given that the age of Ramesh would be twice the age of Rahim when Ramesh is 9 years older than his present age and Rahim is 9 years younger than his present age.
$ \Rightarrow \left( {x + 9} \right) = 2\left( {y - 9} \right)$
Simplifying the above equation we get
$ \Rightarrow 2y - x = 27$
Solving for $y$ (or we can also solve for $x$)
From equation (1) we can substitute $x = \left( {\frac{5}{7}} \right)y$, then
$ \Rightarrow 2y - \left( {\frac{5}{7}} \right)y = 27$
$ \Rightarrow y\left( {\frac{{14 - 5}}{7}} \right) = 27$
$$ \Rightarrow y = \left( {\frac{{27 \times 7}}{9}} \right)$$
$ \Rightarrow y = 21$
Substituting $y$ value in equation (1) we get
$ \Rightarrow x = \frac{5}{7} \times 21 = 15$
$\therefore $The age of Ramesh is 15 years and the age of Rahim is 21 years.
Note: While solving the problems based on ages we have to read and understand the problem carefully. We have to identify the logical relations given to form equations in terms of variables. Then solve the equations to get the values for variables which will give us their ages.
Let the present age of Ramesh be $x$ and the present age of Rahim be $y$.
It is given that the ratio of ages of Ramesh and Rahim =5:7
$ \Rightarrow \frac{x}{y} = \frac{5}{7}$ .... (1)
It is given that the age of Ramesh would be twice the age of Rahim when Ramesh is 9 years older than his present age and Rahim is 9 years younger than his present age.
$ \Rightarrow \left( {x + 9} \right) = 2\left( {y - 9} \right)$
Simplifying the above equation we get
$ \Rightarrow 2y - x = 27$
Solving for $y$ (or we can also solve for $x$)
From equation (1) we can substitute $x = \left( {\frac{5}{7}} \right)y$, then
$ \Rightarrow 2y - \left( {\frac{5}{7}} \right)y = 27$
$ \Rightarrow y\left( {\frac{{14 - 5}}{7}} \right) = 27$
$$ \Rightarrow y = \left( {\frac{{27 \times 7}}{9}} \right)$$
$ \Rightarrow y = 21$
Substituting $y$ value in equation (1) we get
$ \Rightarrow x = \frac{5}{7} \times 21 = 15$
$\therefore $The age of Ramesh is 15 years and the age of Rahim is 21 years.
Note: While solving the problems based on ages we have to read and understand the problem carefully. We have to identify the logical relations given to form equations in terms of variables. Then solve the equations to get the values for variables which will give us their ages.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
