1. Variations table problems

2. Rules for calculating Variations
In direct variation,
= Constant
In inverse variation, xy = constant
Let us see some examples of how
= constant in direct variation
and xy = constant in inverse variation.

3. Direct variation Lets use x for bigger number and y for smaller number
Look at the table given below:
Weekly expenses x
2000
4000
6000
8000
No of people in the camp y 50
100
150
200
We see that x increases(↑ ), y also increases (↑ ).
Next we shall find the ratio of ‘no of people in the camp’ to ‘weekly expenses’.
=40 = constant
= 40 = constant , Thus they are in direct variation
Lets use x for bigger number and
y for smaller number

4. Inverse variation Look at the table given below: Speed x 2 3 4 5
Time taken y 30 20 15 12
We see that speed x increases (↑ ), Time taken y decreases (↓).
Next we shall find the product of Speed and Time taken.
‘Speed’ x ‘Time taken’ = xy = 2 x 30 = 3 x 20 = 4 x 15 = 5 x 12 = 60 = constant
We see that , xy = 60 = constant, Thus they are in inverse variation

5. Example 1: If x varies directly as y, complete the given tables:2 5 7 9 11 y 4 10 a 18 b
Solution:
Given: x varies directly as y
∴ In direct variation
Lets find the constant and use it to find a and b
and now lets find the unknown value a and b
X 7 =
∴ a = 14 14
X 7
X 11
∴ b = 22 =
Ans: a = 14 , b = 22
X 11 22

6. Example 2: If x varies inversely as y, complete the given tables:1 2 3 4 y 24 12 a b
Solution:
Given: x varies inversely as y
∴ In Inverse variation xy = constant
Lets find the constant and use it to find a and b
xy = 1 x 24 = 2 x 12 = 24 = constant
Constant=24 and now, we try to find the unknown value a and b
3 x a = 24
3 x 8 = 24
∴ a = 8
4 x b = 24
4 x 6 = 24
∴ b = 6
Ans: a = 8 and b = 6

7. Try these If x varies directly as y, complete the given tables: X 9 1821 b y 3 6 5 7
2. If x varies inversely as y, complete the given tables: X 1 2 3 4 6 Y 36 18 a 9 b