In which of the following case, do the quantities vary directly with each other

(a)

x	0.5	2	8	32
y	2	8	32	128

(b)

p	1	2	3	4
q	1	2	3	4

(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

Solution:

If two variables say x and y are directly proportional then:

x/y = k

On examining the data given above it is evident that only the table (a) demonstrates direct proportion because

x/y = 0.5/2 = 2/8 = 8/32 = 32/128 = k = 1/4

p/q = 1²/1³ ≠ 2²/2³ ≠ 3²/3³ ≠ 4²/4³ ≠ k

r/s = 2/25 ≠ 5/10 ≠ 10/5 ≠ 25/2 ≠ 50/0.5 ≠ k

u/v = 2/18 ≠ 4/9 ≠ 6/6 ≠ 9/4 ≠ 12/3 ≠ k

In none of the tables in (b), (c ) and (d) such a behaviour is observed i.e. the proportionality constant k is observed.

✦ Try This: In which of the following case, do the quantities vary directly with each other?

a)

x	0.5	1	1	0.10
y	10	5	15	50

(b)

p	1⁴	2⁴	3⁴	4⁴
q	1	2	3	4

(c)

r	75	125	25	10	40
s	15	25	5	2	8

(d)

u	3	8	6	2	18
v	24	9	12	36	4

On examining the data given above it is evident that only the table (a) demonstrates direct proportion because

x/y = 0.5/10 ≠ 1/5 ≠ 1/15 ≠ 0.10/50 ≠ k

p/q = 1⁴/1³ ≠ 2⁴/2³ ≠ 3⁴/3³ ≠ 4⁴/4³ ≠ k

r/s = 75/15 = 125/25 = 25/5 = 10/2 = 40/8 = k = 5

u/v = 3/24 ≠ 8/9 ≠ 6/12 ≠ 2/36 ≠ 18/4 ≠ k

In none of the tables in (a), (b) and (d) such a behaviour is observed i.e. the proportionality constant k is observed.

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 7

Summary:

Only in case (a), do the quantities vary directly with each other and the constant of proportionality k = 1/4

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