Questions & Answers

Question

Answers

a.3:5

b.2:5

c.2:3

d.3:4

Answer
Verified

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 $\dfrac{{x - 5}}{{2x - 5}}$. â€¦â€¦â€¦â€¦..(1)

Step 3: It is also given that, five years back the ratio was $1:3$.

This can be written as $\dfrac{1}{3}$â€¦â€¦â€¦(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 $3:5$

After finding the ages we just canâ€™t stop by leaving the ratio at 15:25. We need to reduce it to its simpler form in order to get full marks.