Both x and y are in direct proportion, then 1/x and 1/y are
(a) in indirect proportion
(b) in inverse proportion
(c) neither in direct nor in inverse proportion
(d) sometimes in direct and sometimes in inverse proportion

Solution:

If x and y are in direct proportion then we can write:

x/y = k — (1)

x = yk

If x is replaced by 1/x and y replaced by 1/y then we get:

(1/x)/(1/y) = y/x — (2)

From (1) x/y = k, Therefore,

y/x = 1/k

From (2) & (3) we have,

(1/x)/(1/y) = y/x = 1/k

There 1x and 1/y are in inverse proportion.

✦ Try This: In the table below y and x are in direct proportion. Verify that y/x are in inverse proportion.

x	0.5	2	8	32
y	2	8	32	128

From the table it is observed:

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

Now let us prepare the table of 1/y and 1/x

1/x	2	0.5	0.125	0.03125
1/y	0.5	0.125	0.03125	0.0078125

(1/y)/(1/x) = 0.5/2 = 0.125/0.5 = 0.03125/0.125 = 0.0078125/0.03125 = 0.25 = 1/4 = 1/k

Also,

0.5/2 = 0.125/0.5 = 0.03125/0.125 = 1/4 = 1/k

Hence it is verified that if y and x are in direct proportion then 1/y and 1/x are in inverse proportion

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 10

Both x and y are in direct proportion, then 1/x and 1/y are (a) in indirect proportion, (b) in inverse proportion, (c) neither in direct nor in inverse proportion, (d) sometimes in direct and sometimes in inverse proportion

Summary:

If both x and y are in direct proportion, then 1/x and 1/y are in inverse proportion

☛ Related Questions: