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Grade 8 - Mathematics
2.12 Direct Proportion - I

  • Two variables are in direct proportion to one another if they are always in the same ratio.
  • If two variables x and y are vary in such a way that their ratio x/y is a constant(k). Then x and y are said to vary directly or in direct variation "k" is called the constant of variation.
  • \ If variables x and y are directly then x/y = k or x=ky.
  • This is denoted by xy.
Example:
yx, and constant of variation is 6. Find y, when x=3, find x, when y=24.

Solution:
Since yx, we have y = kx
But k = 6 y = 6x
If x = 3 y = 6*3 = 18
If y = 25 25 = 3x x = 25/3.

Example:
If 4 bottles of milk cost $2, how many bottles can you buy for $8?
Solution:
You can write this in proportion as
4:2 :: x:8
or
4/2 = x/8
Cross multiplying we get
2x = 32
x = 16 Answer: 16 bottles


Directions: Solve the following problems. Also write atleast 10 examples of your own.
Q 1: y is directly proportional to x, and constant of variation is 8. Find y when x=5.
None of these
40
56
30

Q 2: y is directly proportional to x, and constant of variation is 4. Find x, when y = 5.
None of these
46
5/4
4/5

Q 3: y is directly proportional to x, and constant of variation is 7. Find y, when x = 4.
None of these
38
48
28

Q 4: y is directly proportional to x, and constant of variation is 15. Find x, when y = 30.
None of these
4
2
6

Q 5: The cost of 10 books is $80. Find the value of 15 books.
$120
$250
$160
$150

Q 6: On a map, 1/2 inch = 10 miles. How many miles apart are two towns that are 3 1/4 inches apart on the map?
67
72
45
54

Q 7: Monthly expenditure of a family of 4 members is $2,800, what is the expenditure if there are 3 members in a family.
$2,800
None of these
$1,600
$2,100

Q 8: If 18 tonnes of grass is needed for 12 cattle. How many tonnes of grass is required for 30 cattle.
35 tonnes
45 tonnes
40 tonnes
25 tonnes

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Question 10: This question is available to subscribers only!


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