Question

Which of the following follows indirect variations between X and Y?

• A.

  X	3	4	5	6
  Y	20	15	12	10

• B.

  X	9	6	3	2
  Y	10	15	30	45

• C.

  X	2	4	6	8
  Y	12	6	4	3

• D.

  X	2	4	5	6
  Y	50	25	20	25

Answer 1

Answer: (A), (B), (C)

X	2	4	6	8
Y	12	6	4	3

Concept: Two quantities X and Y are said to be in inverse proportion if an increase in X causes a proportional decrease in Y and vice-versa, in such a manner that the product of their corresponding values remains constant. That is, XY = k where k is a positive number.

Using this concept satisfy the values associated with options. If XY = k is satisfied for options individually then X and Y of that particular option is in inverse proportion.

Option A :

X	3	4	5	6
Y	20	15	12	10

As X increases, Y decreases.
$\Rightarrow 20\times 3=4\times 15=5\times 12=6\times 10=60$
Hence, $X\propto \frac{1}{Y}$

Option B:

X	9	6	3	2
Y	10	15	30	45

As X decreases, Y increases
$\Rightarrow 9\times 10=6\times 15=3\times 30=2\times 45=90$
Hence, $X\propto \frac{1}{Y}$

Option C:

X	2	4	6	8
Y	12	6	4	3

As X increases, Y decreases.
$\Rightarrow 2\times 12=4\times 6=6\times 4=8\times 3=24$
Hence, $X\propto \frac{1}{Y}$

Option D :

X	2	4	5	6
Y	50	25	20	25

As X increases, Y decreases.
$\Rightarrow 2\times 50=4\times 25=5\times 20=100\ne 6\times 25=150$
Hence, X is not inversely proportional to Y.