Answer
423.9k+ views
Hint: We need to assume the present ages to be $x,2x$, and from this, we can say that the ages of the brothers before 5 years are $x - 5$ and $2x - 5$. Find the ratio between these two and equate with a given ratio and we will get a linear equation in x. solving which we can get the present age and adding 5 to the present age gives the age after five years
Complete step by step answer:
Step 1:It is given that the ratio of the present ages of two brothers is $1:2$
From this, let us assume the ages to be $x,2x$
Step 2:Five years before the ages of the brothers will be $x - 5$ and $2x - 5$ respectively.
Let the ratio of these ages be $\dfrac{{x - 5}}{{2x - 5}}$. …………..(1)
Step 3: It is also given that, five years back the ratio was $1:3$.
This can be written as $\dfrac{1}{3}$………(2)
Step 4:Now by equating (1) and(2), we get
$ \Rightarrow \dfrac{{x - 5}}{{2x - 5}} = \dfrac{1}{3}$
By cross multiplying we get,
$\begin{gathered}
\Rightarrow 3(x - 5) = 1(2x - 5) \\
\Rightarrow 3x - 15 = 2x - 5 \\
\end{gathered} $
Lets bring the terms to one side and the constants to the other side
$\begin{gathered}
\Rightarrow 3x - 2x = 15 - 5 \\
\Rightarrow x = 10 \\
\end{gathered} $
Step 5:Now, we have that $x = 10$, which is the present age of one of the brothers.
From this,lets calculate the age of the other brother (i.e.) $2x = 2(10) = 20$
Step 6: We are asked to find the ratio of the ages after five years.
The ages of the brothers after five years are $x + 5$ and $2x + 5$
$\begin{gathered}
\Rightarrow x + 5 = 10 + 5 = 15 \\
\Rightarrow 2x + 5 = 2(10) + 5 = 20 + 5 = 25 \\
\end{gathered} $
Step 7: Now lets find the ratio of the ages
$ \Rightarrow \dfrac{{15}}{{25}}$
And now we need to simply the above fraction to the simplest form
$ \Rightarrow \dfrac{{5*3}}{{5*5}} = \dfrac{3}{5}$
Therefore the ratio of ages after five years is $3:5$
The answer is option a.
Note: When the ratio of two quantities is given like the ages of two persons is 2:5. That does not mean that the ages are 2 and 5. Most of the students make a mistake here.
After finding the ages we just can’t stop by leaving the ratio at 15:25. We need to reduce it to its simpler form in order to get full marks.
Complete step by step answer:
Step 1:It is given that the ratio of the present ages of two brothers is $1:2$
From this, let us assume the ages to be $x,2x$
Step 2:Five years before the ages of the brothers will be $x - 5$ and $2x - 5$ respectively.
Let the ratio of these ages be $\dfrac{{x - 5}}{{2x - 5}}$. …………..(1)
Step 3: It is also given that, five years back the ratio was $1:3$.
This can be written as $\dfrac{1}{3}$………(2)
Step 4:Now by equating (1) and(2), we get
$ \Rightarrow \dfrac{{x - 5}}{{2x - 5}} = \dfrac{1}{3}$
By cross multiplying we get,
$\begin{gathered}
\Rightarrow 3(x - 5) = 1(2x - 5) \\
\Rightarrow 3x - 15 = 2x - 5 \\
\end{gathered} $
Lets bring the terms to one side and the constants to the other side
$\begin{gathered}
\Rightarrow 3x - 2x = 15 - 5 \\
\Rightarrow x = 10 \\
\end{gathered} $
Step 5:Now, we have that $x = 10$, which is the present age of one of the brothers.
From this,lets calculate the age of the other brother (i.e.) $2x = 2(10) = 20$
Step 6: We are asked to find the ratio of the ages after five years.
The ages of the brothers after five years are $x + 5$ and $2x + 5$
$\begin{gathered}
\Rightarrow x + 5 = 10 + 5 = 15 \\
\Rightarrow 2x + 5 = 2(10) + 5 = 20 + 5 = 25 \\
\end{gathered} $
Step 7: Now lets find the ratio of the ages
$ \Rightarrow \dfrac{{15}}{{25}}$
And now we need to simply the above fraction to the simplest form
$ \Rightarrow \dfrac{{5*3}}{{5*5}} = \dfrac{3}{5}$
Therefore the ratio of ages after five years is $3:5$
The answer is option a.
Note: When the ratio of two quantities is given like the ages of two persons is 2:5. That does not mean that the ages are 2 and 5. Most of the students make a mistake here.
After finding the ages we just can’t stop by leaving the ratio at 15:25. We need to reduce it to its simpler form in order to get full marks.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)