If a and b vary inversely to each other, then find the values of p, q, r ; x, y, z and l, m, n.
(i) a 6 8 q 25
b 18 p 39 r
(ii) a 2 y 6 10
B x 12.5 15 z
(iii) a l 9 n 6
b 5 m 25 10

Solution:

(i)

a 6 8 q 25
b 18 p 39 r

If a and b are inversely related then

a ∝ 1/b

ab = k

Therefore,

6 × 18 = 8 × p = q × 39 = 25 × r

8p = 6 × 18

p = (6 × 18)/8 = (3 × 9)/2 = 27/2

39q = 6 × 18

13q = 2 × 18

q = 36/13

25r = 6 × 18

r = 108/25

(ii)

a 2 y 6 10
b x 12.5 15 z

If a and b are inversely related then

a ∝ 1/b

ab = k

Therefore,

6 × 15 = 2 × (x)

x = (6 × 15)/2

x = 3 × 15

x = 45

Similarly

y × 12.5 = 6 × 15

y = (6 × 15)/12.5

y = (6 × 3)/2.5

y = 36/5 = 7.2

Finally

10z = 6 × 15

z = (6 × 15)/10

z = 9

(iii)

a l 9 n 6
b 5 m 25 10

If a and b are inversely related then

a ∝ 1/b

ab = k

Therefore,

5l = 6 ×10

5l = 60

l = 12

Also,

9m = 6 × 10

m = 20/3

Similarly,

25n = 6 × 10

5n = 6 × 2

n = 12/5

✦ Try This: If a and b vary directly with each other, then find the values of p, q, r ; x, y, z and l, m, n.

(i)

a 2 5 q 4
b 6 p 27 r

(ii)

a 2 y 6 8
b x 24 48 z

(iii)

a l 9 n 2
b 50 m 25 10

(i) a/b = k

2/6 = k

1/3 = k

Therefore:

1/3 = 5/p

p = 15;

q/27 = 1/3

q = 27/3 = 9;

4/r = 1/3

r = 12

(ii) k = 6/48 = 1/8

2/x = 1/8

x = 16

y/24 = 1/8

y = 24/8 = 3

8/z = 1/8

z = 64

(iii) k = 2/10 = 1/5

l/50 = 1/5

l = 10

9/m = 1/5

m = 45

n/25 = 1/5

n = 5

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 78

If a and b vary inversely to each other, then find the values of p, q, r ; x, y, z and l, m, n (i) a 6 8 q 25 b 18 p 39 r (ii) a 2 y 6 10 b x 12.5 15 z (iii) a l 9 n 6 b 5 m 25 10

Summary:

If a and b vary inversely to each other, then the values of p = 27/2, q=36/13, r=108/25; x=45, y = 7.2, z=9 and l=12, m=20/3, n=12/5

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