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Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
$ x$  $2$ $ 5$ $ 25$
$ y$  $25$  $10$  $m$

If $x$ & $y$ are in inverse proportion, find m

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 25 = 50 = K$
now, $25\times m = 50$
$\therefore m = 2$
Answer is option B

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
 $x$  $2$ $ 3$ $ 5$ $ 6$ $10$
$ y$  $15$  $10$ $ b$  $5$ $ 3$

Identify the inverse proportional quantities.

  1. $4$
  2. $5$
  3. $6$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 15 = 30 = K$
now, $5\times b = 30$
$\therefore b = 6$
Answer is option C

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

If $\displaystyle \frac { a }{ b } -\frac { c }{ d } =0$ and bc=7, then determine the true statement among the following.

  1. a and b are directly proportional.

  2. a and c are inversely proportional.

  3. a and d are inversely proportional.

  4. b and c are directly proportional.

  5. c and d are inversely proportional.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac{a}{b}-\dfrac{c}{d}=0$

$\Rightarrow \dfrac{a}{b}=\dfrac{c}{d}$
$\Rightarrow ad=bc$
According to the question $bc=7$
$\therefore ad=7$
Then $a$ and $d$ are inversely proportional to eachother.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

Which of the following are in inverse proportion?

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

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

  3. Area of cultivated land and the crop harvested.

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

  5. The population of a country and the area of land per person.
Reveal answer Fill a bubble to check yourself
A,D,E Correct answer
Explanation

Inverse proportion is a relation between two quantities such that one increases in proportion as the other decreases i.e. If $x$ increases as $y$ decreases, $x \alpha \dfrac{1}{y}$ 


In option A, if the no. of workers are increased then the time required to do the job will decrease, likewise if no. of workers decrease, then time to do the same job will increase i.e. no. of workers and time to do the job are inversely proportional to each other.


Similarly is the option D and E where the time taken to complete the journey is inversely proportional to the speed of vehicle and population is inversely proportional to area of the land respectively, are both examples of inverse proportion. 

So, the answer is A, D, E.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

The length of a pendulum varies inversely as the square of the number of beats it makes per minute. If a pendulum, $65$ cm long, makes $27$ beats per minute, then the length of the pendulum that makes $24$ beats per minutes is 

  1. $91$ cm
  2. $85$ cm
  3. $81$ cm
  4. $71$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Length $\alpha \cfrac{1}{(\text {No. of beats} )^2}$
$ \Rightarrow L = \cfrac{k}{\text {(beat)}^2}$, where $k$ is constant.
$\Rightarrow 65 = \cfrac{k}{(27)^2}$
$\Rightarrow k = 65 \times (27)^2$ 
Also, $k=L\times(24)^2$
$\Rightarrow 65 \times (27)^2= L \times(24)^2$
$\Rightarrow L = 81 cm $(approx)