Question

For the given table, identify the relation between $x$ and $y$ and select the values of $a,b,c$ and $d$.



Note: There is a constant increase for the elements of $x$.

• A. $a=20$, $b=36$, $c=25$ and $d=50$
• B. $a=36$, $b=20$, $c=24$ and $d=48$

Answer 1

The correct option is B $a=36$, $b=20$, $c=24$ and $d=48$

To identify the relation between $x$ and $y$, we take the given values of $x=22$ and $y=44$
And we see that $44=2\times 22$, i.e., $y=2\times x$

Thus, when $x=18$, $y=2\times 18=36$
Therefore, $a=36$

Also, $x$ increases by $2$ units as we go down the table. Hence the difference between two successive values of $x$ is always constant ($=2$).
Therefore,
$b-18=22-b$
$b+b=22+18$
$2b=40$
$b=20$
Thus there is a difference of $2$ units in each element of $x$.

When $x=20$, $y=40$ which satisfies the derived equation.

Again, because of the constant increase in $x$, $c=22+2=24$
and from our equation, we can say that $d=2\times 24=48$

Therefore, $a=36;b=20;c=24;d=48$.
So, option (b.) is correct.