Answer

Verified

475.8k+ 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

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The polyarch xylem is found in case of a Monocot leaf class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Casparian strips are present in of the root A Epiblema class 12 biology CBSE