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# In which of the following case, do the quantities vary directly with each other

(a)

x |
0.5 |
2 |
8 |
32 |

y |
2 |
8 |
32 |
128 |

(b)

p |
1 |
2 |
3 |
4 |

q |
1 |
2 |
3 |
4 |

(c)

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

s |
25 |
10 |
5 |
2 |
0.5 |

(d)

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

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

**Solution:**

If two variables say x and y are directly proportional then:

x/y = k

Where k = proportionality constant

On examining the data given above it is evident that only the table (a) demonstrates direct proportion because

x/y = 0.5/2 = 2/8 = 8/32 = 32/128 = k = 1/4

p/q = 1²/1³ ≠ 2²/2³ ≠ 3²/3³ ≠ 4²/4³ ≠ k

r/s = 2/25 ≠ 5/10 ≠ 10/5 ≠ 25/2 ≠ 50/0.5 ≠ k

u/v = 2/18 ≠ 4/9 ≠ 6/6 ≠ 9/4 ≠ 12/3 ≠ k

In none of the tables in (b), (c ) and (d) such a behaviour is observed i.e. the proportionality constant k is observed.

**✦ Try This: **In which of the following case, do the quantities vary directly with each other?

a)

x |
0.5 |
1 |
1 |
0.10 |

y |
10 |
5 |
15 |
50 |

(b)

p |
1⁴ |
2⁴ |
3⁴ |
4⁴ |

q |
1 |
2 |
3 |
4 |

(c)

r |
75 |
125 |
25 |
10 |
40 |

s |
15 |
25 |
5 |
2 |
8 |

(d)

u |
3 |
8 |
6 |
2 |
18 |

v |
24 |
9 |
12 |
36 |
4 |

On examining the data given above it is evident that only the table (a) demonstrates direct proportion because

x/y = 0.5/10 ≠ 1/5 ≠ 1/15 ≠ 0.10/50 ≠ k

p/q = 1⁴/1³ ≠ 2⁴/2³ ≠ 3⁴/3³ ≠ 4⁴/4³ ≠ k

r/s = 75/15 = 125/25 = 25/5 = 10/2 = 40/8 = k = 5

u/v = 3/24 ≠ 8/9 ≠ 6/12 ≠ 2/36 ≠ 18/4 ≠ k

In none of the tables in (a), (b) and (d) such a behaviour is observed i.e. the proportionality constant k is observed.

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

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 7**

## In which of the following case, do the quantities vary directly with each other

**Summary:**

Only in case (a), do the quantities vary directly with each other and the constant of proportionality k = 1/4

**☛ Related Questions:**

- Which quantities in the following case vary inversely with each other (a) x and y, (b) p and q, (c) . . . .
- 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 . . . .

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