Question

Which of the following is not a case of direct proportion?

Height of the object and the length of the shadow formed


Speed and time for a particular distance


Distance and time taken for a uniform speed


None of the above​

Answer 1

Two quantities x and y are said to be in direct proportion if they

increase or decrease together in such a manner that the ratio of

their corresponding values remains constant. That is, x

y

= k where

k is a positive number, if x and y are in direct proportion or vary

directly. In case of direct proportion, if y1, y2 are the values of y

corresponding to the values x1, x2 of x respectively, then 1 2

1 2

x x

y y  .

• 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. That is, xy = k where k is a positive number, if x

and y are in inverse proportion. In this case, if y1, y2 are the values

of y corresponding to the values x1, x2 of x respectively, then x1 y1=

x2 y2 or

x y

x y

1 1

2 2



• Quantities increasing or decreasing together need not always be

in direct proportion, same in the case of inverse proportion.

• When two quantities x and y are in direct proportion (or vary directly),

they are written as x ∝ y. Symbol “∝” stands for ‘is proportional to’.

When two quantities x and y are in inverse proportion (or vary

inversely) they are written as x ∝ 1

y

.