# 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

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