Tag: maths

Questions Related to maths

$ x$  $2$ $ 5$ $ 25$
$ y$  $25$  $10$  $m$

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

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
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

Which of the following $x$ & $y$ are in inverse proportion?

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

  1. $\dfrac{x}{y}=K$

  2. $x+y=K$

  3. $x-y=K$

  4. $xy=K$

Show answer
Correct Option: D
Explanation:
 $\dfrac{x}{y}=k$$\implies x=ky$$\implies x\alpha y$  $x+y=k$$\implies x=k-y$  $x-y=k$$\implies x=k+y$ $xy=k$$\implies x=\dfrac{k}{y}$$\implies x\alpha \dfrac{1}{y}$ 

Answer $(D)$

 $x$  $2$ $ 3$ $ 5$ $ 6$ $10$
$ y$  $15$  $10$ $ b$  $5$ $ 3$

Identify the inverse proportional quantities.

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

  1. $4$

  2. $5$

  3. $6$

  4. $10$

Show answer
Correct Option: C
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

Find inverse proportionaly constant if $x$ and $y$ are in inverse proportion.

$x$ $9$ $6$ $3$ $18$
$y$ $2$ $3$ $6$ $1$
maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

  1. $9$

  2. $18$

  3. $27$

  4. $30$

Show answer
Correct Option: B
Explanation:

$\because x$ and $y$ are inverse porportion
$\therefore x \times y = k \Rightarrow 9\times 2 = 6\times 3 = 3\times 6 = 18\times 1 = 18 = k$

A work is done by $10$ workers in $6$ hours? How many workers will be required to do the same work in $4$ hrs?

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

  1. $10$

  2. $15$

  3. $20$

  4. None of these

Show answer
Correct Option: B
Explanation:

It is inverse variation.
$6\times 10 = 4\times x$
$\Rightarrow x = \dfrac {6\times 10}{4} = 15\ workers$

$35$ workers can build a house in $16$ days. How many days will $28$ workers working at the same rate take to build the same house?

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

  1. $16\ days$

  2. $28\ days$

  3. $20\ days$

  4. $10\ days$

Show answer
Correct Option: C
Explanation:

By inverse proportion,

$28\times x = 35\times 16$

$x = \dfrac {35\times 16}{28} = 20\ days$

Four pipes can fill a tank in $70$ min. How long will it take to fill the tank by $7$ pipes?

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

  1. $20\ min$

  2. $35\ min$

  3. $40\ min$

  4. None of these

Show answer
Correct Option: C
Explanation:

By the principle of inverse proportion
$4\times 70 = 7\times x$
$\Rightarrow x = \dfrac {4\times 70}{7} = 40\ min$

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

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

  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.

Show answer
Correct Option: C
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.

Which of the following are in inverse proportion?

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

  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.

Show answer
Correct Option: A,D,E
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.

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 

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

  1. $91$ cm

  2. $85$ cm

  3. $81$ cm

  4. $71$ cm

Show answer
Correct Option: C
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)