# Which quantities in the following case vary inversely with each other

(a)

x |
0.5 |
2 |
8 |
32 |

y |
2 |
8 |
32 |
128 |

(b)

p |
1² |
2² |
3² |
4² |

q |
1³ |
2³ |
3³ |
4³ |

(c)

r |
2 |
5 |
10 |
25 |
50 |

s |
25 |
9 |
6 |
3 |
0.5 |

(d)

u |
2 |
4 |
6 |
9 |
12 |

v |
18 |
9 |
6 |
4 |
3 |

(a) x and y

(b) p and q

(c) r and s

(d) u and v

**Solution:**

When x and y are inversely proportional then we can write:

xy = k

Where k is constant of proportionality

Now let us examine the the data and discover the inverse proportionality

xy = 0.5 × 2 ≠ 2 × 8 ≠ 8 × 32 ≠ 32 × 128 ≠ k

pq = 1² × 1³ ≠ 2² × 2³ ≠ 3² × 3³ ≠ 4² × 4³ ≠ k

rs = 2 × 25 ≠ 5 × 9 ≠ 10 × 5 ≠ 25 × 3 ≠ 50 × 0.5 ≠ k

uv = 2 × 18 = 4 × 9 = 6 × 6 = 9 × 4 = 12 × 3 = k = 36

In none of the tables in (a), (b) and (c) such a behaviour is not observed i.e. the proportionality constant k is observed.

**✦ Try This: **Which quantities below vary inversely with each other?

(a)

x |
0.5 |
8 |
4 |
20 |

y |
2 |
0.125 |
0.25 |
0.05 |

(b)

p |
1² |
2² |
3² |
4² |

q |
1⁴ |
2⁴ |
3⁴ |
4⁴ |

(c)

r |
2 |
5 |
10 |
25 |
10 |

s |
18 |
45 |
90 |
225 |
150 |

(d)

u |
4 |
2 |
4 |
5 |
7 |

v |
18 |
9 |
6 |
4 |
3 |

(a) x and y (b) p and q (c) r and s (d) u and v

When x and y are inversely proportional then we can write:

xy = k

Where k is constant of proportionality

Now let us examine the the data and discover the inverse proportionality

xy = 0.5 × 2 = 2 × 0.125 = 4 × 0.25 = 20 × 0.05 = 1 = k

pq = 1² × 1⁴ ≠ 2² × 2⁴ ≠ 3² × 3⁴ ≠ 4² × 4⁴ ≠ k

rs = 2 × 18 ≠ 5 × 45 ≠ 10 × 90 ≠ 25 × 225 ≠ 10 × 150 ≠ k

uv = 4 × 18 ≠ 2 × 9 ≠ 6 × 6 ≠ 4 × 6 ≠ 3 × 4 ≠ 7 × 3 ≠ k

Answer is (a)

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

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

## Which quantities in the following case vary inversely with each other (a) x and y, (b) p and q, (c) r and s, (d) u and v

**Summary:**

The quantities which vary inversely with each other are u and v where uv = 36

**☛ Related Questions:**

- Which of the following vary inversely with each other (a) speed and distance covered, (b) distance c . . . .
- Both x and y are in direct proportion, then 1/x and 1/y are (a) in indirect proportion, (b) in inver . . . .
- Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her sch . . . .

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