# If two quantities p and q vary inversely with each other, then

(a) p/q remains constant

(b) p + q remains constant

(c) p × q remains constant

(d) p - q remains constant

**Solution: **

If two quantities p and q vary inversely with each other, then we can write,

p ∝ 1/q

which implies

pq = k = proportionality constant

Therefore,

If two quantities p and q vary inversely with each other, then p × q remains constant.

**✦ Try This:** If two quantities p and q vary inversely with each other, then verify the following using a suitable example: (a) p/q remains constant, (b) p + q remains constant, (c) p × q remains constant, (d) p - q remains constant

The table shows the quantities p and q which are inversely related.

p |
0.5 |
8 |
4 |
20 |

q |
2 |
0.125 |
0.25 |
0.05 |

(a) p/q = 0.5/2 ≠ 8/0.125 ≠ 4/0.25 ≠ 20/0.25 ≠ k ≠ constant

(b) p + q = 0.5 + 2 ≠ 8 + 0.125 ≠ 4 + 0.25 ≠ 20 + 0.05 ≠ k ≠ constant

(c) p × q = 0.5 × 2 = 8 × 0.125 = 4 × 0.25 = 20 × 0.05 = k = 1

(d) p - q = 0.5 - 2 ≠ 8 - 0.125 ≠ 4 - 0.25 ≠ 20 - 0.05 ≠ k ≠ constant

The relationship which is applicable when quantities p and q are inversely proportional is p × q is a constant.

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 14**

## If two quantities p and q vary inversely with each other, then (a) p/q remains constant, (b) p + q remains constant, (c) p × q remains constant, (d) p - q remains constant

**Summary:**

If two quantities p and q vary inversely with each other, then p × q remains constant

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