Question

Which quantities in the question vary inversely with each other?

• A.

  x	0.5	2	8	32
  y	2	8	32	128

• B.

  p	12	22	32	42
  q	13	23	33	43

• C.

  r	2	5	10	25	50
  s	25	10	5	2	0.5

• D.

  u	2	4	6	9	12
  v	18	9	6	4	3

Answer 1

The correct option is D

u	2	4	6	9	12
v	18	9	6	4	3

Explanation for the correct option:

Option : D :

u	2	4	6	9	12
v	18	9	6	4	3

We know that $a$ and $b$ vary inversely if $ab=k$

Here,

$u$ and $v$ vary inversely as the product of each pair is same. That is

$$\begin{gathered} 2\times 18=36 \\ 4\times 9=36 \\ 6\times 6=36 \\ 9\times 4=36 \\ 12\times 3=36 \end{gathered}$$

So, $u$ and $v$ vary inversely.

Hence,option(D) is correct answer.

Explanation for the incorrect options.

Option : A:

x	0.5	2	8	32
y	2	8	32	128

The product of pair of $\left(x,y\right)$

$$\begin{gathered} 0.5\times 2=1 \\ 2\times 8=16 \\ \Rightarrow 1\ne 16 \end{gathered}$$

Option : B :

p	12	22	32	42
q	13	23	33	43

The product of pair of $\left(p,q\right)$

$$\begin{gathered} 1^2\times 1^3=1 \\ {2}^2\times 2^3=4\times 8 \\ =32 \\ \Rightarrow 1\ne 32 \end{gathered}$$

Option : C :

r	2	5	10	25	50
s	25	10	5	2	0.5

The product of pair of $\left(r,s\right)$

$$\begin{gathered} 2\times 25=50 \\ 50\times 0.5=25 \\ \Rightarrow 25\ne 50 \end{gathered}$$

Since, the product of each pair of $\left(x,y\right),\left(p,q\right),\left(r,s\right)$ is not the same.

So, all these options are incorrect.

Hence, the correct option is $\mathrm{D}$.