Current Affairs 8th Class

Category : 8th Class

 Direct and Inverse Proportions

• Unitary method:

A method in which the value of a quantity is first obtained to find the value of any required quantity is called unitary method.

• Direct proportion:

(i) 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.

(ii) That is, if \[\frac{X}{Y}=K\] [k is a positive number], then x and y are said to vary directly. In such

• a case if \[{{\operatorname{y}}_{1}}\,and\,{{y}_{2}}\] are the values of y corresponding to the values \[{{\operatorname{x}}_{1\,}}\,and\,{{x}_{2}}\]of z respectively then \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}},\]

• Examples:

(a) As the number of articles increases, their cost increases. Cost is directly proportional to the number of articles.

(b) The more the number of men, the more work is done in a given time. Work done is directly proportional to the number of men working at it.

• Inverse proportion:

(i) Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.

(ii) That is, if xy = k, then x and y are said to vary inversely. In this case, if \[{{\operatorname{y}}_{1}}\,and\,{{y}_{2}}\]are

• the values of y corresponding to the values \[{{\operatorname{x}}_{1}}\,and\,{{x}_{2}}\]of x respectively then

\[{{\operatorname{x}}_{1}}{{y}_{1}}={{x}_{2}}{{y}_{2}}\,or\,\frac{{{x}_{1}}}{{{x}_{2}}}=\frac{{{y}_{2}}}{{{y}_{1}}}\].

• Examples:

(i) The more men employed, the less time it takes to complete a given work. The time taken to finish a work is inversely proportional to the number of persons working at it.

(ii) If speed of car is increased, time taken to cover a given distance decreases. The time taken by any vehicle in covering a certain distance is inversely proportional to the speed of the vehicle.