Which quantities in the following case 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	9	6	3	0.5

(d)

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

(a) x and y

(b) p and q

(c) r and s

(d) u and v

Solution:

When x and y are inversely proportional then we can write:

xy = k

Now let us examine the the data and discover the inverse proportionality

xy = 0.5 × 2 ≠ 2 × 8 ≠ 8 × 32 ≠ 32 × 128 ≠ k

pq = 1² × 1³ ≠ 2² × 2³ ≠ 3² × 3³ ≠ 4² × 4³ ≠ k

rs = 2 × 25 ≠ 5 × 9 ≠ 10 × 5 ≠ 25 × 3 ≠ 50 × 0.5 ≠ k

uv = 2 × 18 = 4 × 9 = 6 × 6 = 9 × 4 = 12 × 3 = k = 36

In none of the tables in (a), (b) and (c) such a behaviour is not observed i.e. the proportionality constant k is observed.

✦ Try This: Which quantities below vary inversely with each other?

(a)

x	0.5	8	4	20
y	2	0.125	0.25	0.05

(b)

p	1²	2²	3²	4²
q	1⁴	2⁴	3⁴	4⁴

(c)

r	2	5	10	25	10
s	18	45	90	225	150

(d)

u	4	2	4	5	7
v	18	9	6	4	3

(a) x and y (b) p and q (c) r and s (d) u and v

When x and y are inversely proportional then we can write:

xy = k

Where k is constant of proportionality

Now let us examine the the data and discover the inverse proportionality

xy = 0.5 × 2 = 2 × 0.125 = 4 × 0.25 = 20 × 0.05 = 1 = k

pq = 1² × 1⁴ ≠ 2² × 2⁴ ≠ 3² × 3⁴ ≠ 4² × 4⁴ ≠ k

rs = 2 × 18 ≠ 5 × 45 ≠ 10 × 90 ≠ 25 × 225 ≠ 10 × 150 ≠ k

uv = 4 × 18 ≠ 2 × 9 ≠ 6 × 6 ≠ 4 × 6 ≠ 3 × 4 ≠ 7 × 3 ≠ k

Answer is (a)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 8

Which quantities in the following case vary inversely with each other (a) x and y, (b) p and q, (c) r and s, (d) u and v

Summary:

The quantities which vary inversely with each other are u and v where uv = 36

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