Page 154 - Start Up Mathematics_8 (Non CCE)

Example 1: In which of the following tables, x and y vary directly? Also, find the constant of variation,
in case of direct variation.

(a) x 2 5 6 8 9 12 (b) x 3 6 2 1 4 10

y 6 15 18 24 27 36 y 6 3 1 2 8 5

2 1 5 1 6 1 8 1 9 1 12 1
Solution: (a) = , = , = , = , = , =
6 3 15 3 18 3 24 3 27 3 36 3
2 5 6 8 9 12 1
fi = = = = = =
6 15 18 24 27 36 3
1
Since, the ratio of the corresponding values of x and y is equal to , x and y are in direct

1 3
variation and the constant of variation is .
3
3 1 6 2 2 2 1 1 4 1 10 2
(b) = , = , = , = , = , =
6 2 3 1 1 1 2 2 8 2 5 1

Since, the ratio of the corresponding values of x and y is not equal, x and y do not vary
directly.

Example 2: Fill in the missing entries, if x and y vary directly.

(a) x 1 ... ... 5 10 30 (b) x 6 9 4.5 ... ... 24

y 2.5 7.5 10 12.5 ... ... y 10 ... 7.5 12.5 20 ...

1 10 2 6 3 4.5 3
Solution: (a) = = (b) = and =
2.5 25 5 10 5 7.5 5
3
Since x and y vary directly, So, is the constant ratio.
x 2 5
\ 1 = fi 5x = 2 × 7.5 Since x and y vary directly,
75. 5 1 95¥
15 \ 9 = 3 fi y = =15
fi 5x = 15.0 fi x = 5 = 3 y 1 5 1 3
1
1
x 3 12.5 3¥
x 2 210 1 = fi x = = 7.5
¥
Similarly, 2 = fi x = = 4 12 5. 5 1 5
10 5 2 5
x 3 20 3¥
2
10 = 2 fi y = 510¥ = 25 20 = 5 fi x = 5 =12
2
y 1 5 1 2 24 3 24 5¥
= fi y = =40
2
30 = 2 fi y = 30 5¥ = 75 y 2 5 3
y 2 5 2 2 \ The missing entries are

3 4 10 9 , 7.5 , 12 , 24 .
So the missing entries are , , 15 12.5 20 40
30 7.5 10 25
and .
75

146