Question

\[X\] is three times as old as $Y,Z$ was twice as old as old \[X\] four year ago. In the four year time, \[X\] will be of $31$ years. What is the present age of $Y$ and $Z$
(A) $9$ years , $46$ years
(A) $9$ years , $50$ years
(A) $10$ years , $46$ years
(D) $10$ years , $50$ years

Answer 1

Hint:This is the simple problem of linear equations. We make equations by using the condition as given in the question by assuming age as variable like \[X\] equals $x$.

Complete step-by-step answer:
Let's assume the age of $X$ is $x$ , $Y = y$ and $Z = z$
[ This is we assume to find age of each person ]
As given in question \[X\] is three times as old as $Y,$
$x = 3y$
And $Z$was twice old as old \[X\] four year ago
So $z - 4 = 2\left( {x - 4} \right)$ [ Given condition tell that four year ago $Z$ was twice old as old \[X\] so first we subtract four from both and multiply $x$ term by two ]
And In the four year time, \[X\] will be of $31$ years
That mean$x + 4 = 31$; [ We assume that present age of $X = x$ so after four year it become 31 year old that’s why we make $x + 4 = 31$ ]
By solving above equation we get
$x = 27$
 Now we have value of $x$ ; by putting this value in $x = 3y$
We get $27 = 3y$
And by solving this $y = 9$.
So age of $Y$ is equal to $9$
Now put the value of $x$ in $z - 4 = 2\left( {x - 4} \right)$
So from this $z - 4 = 2\left( {27 - 4} \right)$
Now $z - 4 = 46$
This become $z = 50$
So age of $Z$ is equal to $50$
The present age of $Y$ and $Z$ is $9$ years and $50$ years

So, the correct answer is “Option B”.

Note:
1. If you are assuming the current age to be $x$, then the age after n years will be $\left( {x + n} \right)$ years.
2. If you are assuming the current age to be $x$, then the age before n years will be $\left( {x - n} \right)$ years.
3. If the age is given in the form of a ratio, for example, $p:q$, then the age shall be considered as $qx$ and $px$
4.If you are assuming the current age to be $x$, then n times the current age will be $\left( {x \times n} \right)$ years
5.If you are assuming the current age to be $x$ , then $\dfrac{1}{n}$of the age shall be equal to $\left( {\dfrac{x}{n}} \right)$years