From the following tables, determine if x and y are in direct proportion or not.
(i) x 3 6 15 20 30
y 12 24 45 60 120
(ii) x 4 7 10 16
y 24 42 60 96
(iii) x 1 4 9 20
y 1.5 6 13.5 30

Solution:

(i)

x	3	6	15	20	30
y	12	24	45	60	120

If variables x and y are in direct proportion then

x/y = k

3/12 = 6/24 ≠ 15/45 = 20/60 ≠ 30/120

Since all the ratios are not same hence we can say that the variables x and y are not in direct proportion

(ii)

x	4	7	10	16
y	24	42	60	96

If variables x and y are in direct proportion then

x/y = k

4/24 = 7/42= 10/60 = 16/96 = 1/6 = k

Since all the ratios are same hence we can say that the variables x and y are in direct proportion

(iii)

x	1	4	9	20
y	1.5	6	13.5	30

If variables x and y are in direct proportion then

x/y = k

1/1.5 = 4/6 = 9/13.5 = 20/30 = 2/3 = k

The ratio k = 2/3 = constant

Since all the ratios are the same we can say that the variables x and y are in direct proportion.

✦ Try This: From the following tables, determine if x and y are in inverse proportion or not.

(i)

x	2	4	6	8	12
y	24	12	8	6	4

(ii)

x	2	5	10	12
y	30	12	6	5

(iii)

x	2	3	4	6
y	24	16	13	7

(i) if Variables x and y are in inverse proportion then:

x ∝ 1/y

x = k/y

xy = k

xy = 2 × 24 = 4 × 12 = 6 × 8 = 8 × 6 = 12 × 4 = 48

Hence the variables x and y are in inverse proportion.

(ii) In table (ii) the variables x and y are related as follows:

xy = 2 × 30 = 5 × 12 = 10 × 6 = 12 × 5 = 60 = k

Hence x and y are in inverse proportion

(iii) In table (iii) the variables x and y are related as follows:

xy = 2 × 24 = 3 × 16 ≠ 4 × 13 ≠ 6 × 7

Since xy is not a constant we conclude that variables x and y are not in inverse relation.

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

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NCERT Exemplar Class 8 Maths Chapter 10 Problem 77

From the following tables, determine if x and y are in direct proportion or not (i) x 3 6 15 20 30 y 12 24 45 60 120 (ii) x 4 7 10 16 y 24 42 60 96 (iii) x 1 4 9 20 y 1.5 6 13.5 30

Summary:

From the following tables, the following tables are the ones in which variables x and y are in direct proportion (ii) x 4 7 10 16 y 24 42 60 96 (iii) x 1 4 9 20 y 1.5 6 13.5 30

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