Question

"Question 1 Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.

Class 8 Direct and Inverse Proportions Page 213"

Answer 1

Direct variation:

If two quantities increase or decrease together in such a manner that the ratio of their corresponding values remain constant, we say  that the two quantities vary  directly.

In other words x and y are said to vary directly if X/y = k , where k is a positive constant.

In direct Proportion
x/y= k

x=ky

So we can find value of k from known values, and then use the formula to calculate the unknown values

 

Inverse variation:

Two quantities x and y are said to vary inversely or indirectly if an increase in x  causes a decrease in y and a decrease in X causes an increase in y in such a way that xy remains constant.

In other words x and y are said to vary indirectly if x y = k, where K is a positive constant.

In inverse Proportion
xy= k

x=k/y

So we can find value of k from known values, and then use the formula to calculate the unknown values

 

When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x∝ 1/y

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Solution:

(i) 

The number of workers on a job and the time to complete the job is in inverse proportion 

because less workers will take more time to complete a work and more workers will take less time to complete the same work.

(ii) 

The time taken for a journey and the distance travelled in a uniform speed is in direct  proportion

(iii) It is a direct proportion because more area of cultivated land will yield more crops.

(iv) 

The time taken for a fixed journey and the speed of the vehicle are inverse proportion because if time is less, speed is more.

v) 

The population of a country and the area of land per person is a inverse proportion. If the population of a country increases, the area of land per person decreases.

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Hope this will help you....

Answer 2

Answer:

Option 2,4 and 5 is the answer.