Question

The ratio of present ages of kunal and deepesh is $3:5$ after 10 years this ratio is $5:7$ .What is the present age of deepesh?

Answer 1

Hint: In such a type of question we have to use the concept of ratio and proportion and from simultaneous equations to get the required answer.

Complete step-by-step answer:
First, we assign unknown variables, say $'x'$ and $'y'$ to the given ratios in order to get the simultaneous equation.
So, let us consider the personal age of kunal as $'x'$ and that of deepesh be $'y'$.
Given that,
$x:y::3:5$
Therefore, $x = \dfrac{{3y}}{5}$ …(1)
Also according to the question we have but given the age after 10years,
That is,
     $\left( {x + 10} \right):\left( {y + 10} \right)::\;5:7.$
$ \Rightarrow x + 10 = \dfrac{{5\left( {y + 10} \right)}}{7}$
$\Rightarrow 7\left( {x + 10} \right) = 5\left( {y + 10} \right)$
$\Rightarrow 7x + 70 = 5y + 50$
$\Rightarrow 7x = 5y - 20$ ……(2)
Now, substituting the value of $x$ which we obtained from the first equation (1) is the second equation (2) we get,
$7\left( {\dfrac{{3y}}{5}} \right) = 5y - 20$
$\Rightarrow \dfrac{{21y}}{5} = 5y - 20$
$\Rightarrow 21y = 25y - 100$

$\Rightarrow 4y = 100$
$\Rightarrow y = \dfrac{{100}}{4} = 25\;{\rm{years}}$

Therefore, option $B = 25$ years is the right answer.

Note :In such a type of question, always use the proportion concept followed by a simultaneous equation , so that it will be solved in a minute or so. Additionally, be careful to increase the age of each and every person by the given years. Like sometimes the question tells that a father is twice the age of his son/daughter presently but obviously after 10 years(say) he will still not be of twice the age.