Observe the following tables and find if x and y are directly proportional: x 6 10 14 18 22 26 30 y 4 8 12 16 20 24 28

From the given table, we have to check whether x and y are in direct variation. x 6 10 14 18 22 26 30 y 4 8 12 16 20 24 28 Two variables x & y are said to be in direct variation if the ratio between x & y is a constant, i.e. x y = k . So let us find the constant ratio in each case. When x = 6 , y = 4 then constant ratio is x y = 6 4 = 3 2 When x = 10 , y = 8 then constant ratio is x y = 10 8 = 5 4 When x = 14 , y = 12 then constant ratio is x y = 14 12 = 7 6 When x = 18 , y = 16 then constant ratio is x y = 18 16 = 9 8 When x = 22 , y = 20 then constant ratio is x y = 22 20 = 11 10 When x = 26 , y = 24 then constant ratio is x y = 26 24 = 13 12 When x = 30 , y = 28 then constant ratio is x y = 30 28 = 15 14 Here, the constant ratio is not same for all values of x and y . Hence, we can state that x and y are not in direct variation.

Following are the car parking charges near a railway station up to 4 h o u r s ₹ 60 8 h o u r s ₹ 100 12 h o u r s ₹ 140 24 h o u r s ₹ 180 Check if the parking charges are in direct proportion to the parking time.

Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. If y 1 , y 2 are the values of y corresponding to the values x 1 , x 2 of x respectively, then x 1 y 1 = x 2 y 2 . Here, 60 4 = 15 , 100 8 = 25 2 , 140 12 = 35 3 , 180 24 = 15 2 4 60 ≠ 8 100 ≠ 12 140 ≠ 24 180 Hence, the parking charges are not directly proportional to the parking time.

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Earn 100

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$ $20$ $17$ $14$ $11$ $8$ $5$ $2$

$y$ $40$ $34$ $28$ $22$ $16$ $10$ $4$

Important Questions on Direct and Inverse Proportions

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>TRY THESE>Q 1

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$	$6$	$10$	$14$	$18$	$22$	$26$	$30$
$y$	$4$	$8$	$12$	$16$	$20$	$x$	$28$

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>TRY THESE>Q 1

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$	$5$	$8$	$12$	$15$	$18$	$20$
$y$	$15$	$24$	$36$	$60$	$72$	$100$

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>TRY THESE>Q 2

Principal $= ₹ 1000$ , Rate $= 8 %$ per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.

Time period	$1$ year	$2$ years	$3$ years
Simple Interest (in $₹$ )
Compound Interest (in $₹$ )

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>EXERCISE>Q 1

Following are the car parking charges near a railway station up to

$4 h o u r s$	$₹ 60$
$8 h o u r s$	$₹ 100$
$12 h o u r s$	$₹ 140$
$24 h o u r s$	$₹ 180$

Check if the parking charges are in direct proportion to the parking time.

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>EXERCISE>Q 2

A mixture of paint is prepared by mixing $1$ part of red pigments with $8$ parts of the base. In the following table, the parts of the base that need to be added is given. Find $a + b + c + d$ .

Parts of Pigment	$1$	$4$	$7$	$12$	$20$
Parts of base	$8$	$a$	$b$	$c$	$d$

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>EXERCISE>Q 3

A mixture of paint is prepared by mixing some parts of red pigments with some parts of base. If

1

part of a red pigment requires

75 ml

of base, how much red pigment(in

ml

) should we mix with

1800 ml

of base?

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>EXERCISE>Q 4

A machine in a soft drink factory fills

840

bottles in six hours. How many bottles will it fill in five hours

?

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MATHEMATICS Textbook for Class VIII>Chapter 13 - Direct and Inverse Proportions>EXERCISE>Q 5

A photograph of a bacteria enlarged $50,000$ times attains a length of $5 c m$ as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged $20,000$ times only, what would be its enlarged length?

Question Image

Observe the following tables and find if x and y are directly proportional: x 20 17 14 11 8 5 2 y 40 34 28 22 16 10 4

Important Questions on Direct and Inverse Proportions

Learn and Prepare for any exam you want !

Observe the following tables and find if $x$ and $y$ are directly proportional:

$x$ $20$ $17$ $14$ $11$ $8$ $5$ $2$

$y$ $40$ $34$ $28$ $22$ $16$ $10$ $4$