Rahim is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90 ° 60 ° _____ _____ _____ Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

Let us assume the values to be determined be as follows Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90 ° 60 ° p q r We know that, x and y are said to be in inverse proportion if y 1 , y 2 are the values of y corresponding to values x 1 , x 2 of x respectively then x 1 y 1 = x 2 y 2 = k Now, 4 × 90 ° = 360 ° = 6 × 60 ° Hence, this is an inverse proportion. The unknown values can be found as follows So, 4 × 90 ° = p × 8 ⇒ p = 4 × 90 ° 8 = 45 ° Similarly, q = 4 × 90 ° 10 = 36 ° and r = 4 × 90 ° 12 = 30 ° The updated table is as shown below Number of spokes 4 6 8 10 12 Angle between a pair of consecutive spokes 90 ° 60 ° 45 ° 36 ° 30 ° Yes, the number of spokes and the angles formed between the pairs of consecutive spokes are in inverse proportion.

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IMPORTANT

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Observe the following table, are $x$ and $y$ inversely proportional to each other?

$x$ $100$ $200$ $300$ $400$

$y$ $60$ $30$ $20$ $15$

Important Questions on Direct and Inverse Proportions

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8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>TRY THESE>Q (iii)

Observe the following table, are $x$ and $y$ inversely proportional to each other?

$x$	$90$	$60$	$45$	$30$	$20$	$5$
$y$	$10$	$15$	$20$	$25$	$30$	$35$

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 1

Do the following is in inverse proportion?

The number of workers on a job and the time to complete the job.

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 1

Do the following is in inverse proportion?

The time taken for a journey and the distance travelled in a uniform speed.

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 1

Which of the following are in inverse proportion?

Area of cultivated land and the crop harvested.

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 1

Do the following is in inverse proportion?

The time taken for a fixed journey and the speed of the vehicle.

EASY

8th Jammu and Kashmir Board

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 1

Do the following is in inverse proportion?

The population of a country and the area of land per person.

HARD

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 2

In a Television game show, the prize money of rupees

1,00,000

is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

Number of winners	$1$	$2$	$4$	$5$	$8$	$10$	$20$
Prize for each winner (in ₹)	$1,00,000$	$50,000$	$\dots .$	$\dots .$	$\dots .$	$\dots .$	$\dots .$

MEDIUM

8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 12 - Direct and Inverse Proportions>Exercise>Q 3

Rahim is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

Question Image

Number of spokes	$4$	$6$	$8$	$10$	$12$
Angle between a pair of consecutive spokes	$90 °$	$60 °$	_____	_____	_____

Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

Observe the following table, are x and y inversely proportional to each other? x 100 200 300 400 y 60 30 20 15

Important Questions on Direct and Inverse Proportions

Learn and Prepare for any exam you want !

Observe the following table, are $x$ and $y$ inversely proportional to each other?

$x$ $100$ $200$ $300$ $400$

$y$ $60$ $30$ $20$ $15$