Tag: inverse proportion

Questions Related to inverse proportion

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.

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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

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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)

Which of the following is an example of indirect proportion?

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

  1. Number of mangoes in a bag and weight of the bag.

  2. Earning and hours worked.

  3. More the speed, lesser the time taken.

  4. None of these.

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Correct Option: C
Explanation:

Indirect proportion: When one quantity increases another quantity decreases.
In option C, if the speed of the vehicle increases then the time taken by it to cover a distance, decreases.

A fort is provisioned for $42$ days. After $10$ days, a reinforcement of $200$ men arrives and the food will now last only $24$ days. How many men were there in the fort?

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

  1. $200$

  2. $600$

  3. $500$

  4. $300$

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Correct Option: B
Explanation:

Let $x$ soldiers had provision for $42$ days in a fort.

After $10$ days: $x$ soldiers will remain with $32$ days of provision
therefore for $(x+200)$ soldiers provision will decrease to $24$ days
therefore By inverse proportion,
$x\times32= (200+x)\times 24$
$\therefore \dfrac{32}{24} = \dfrac{200 + x}{x}$
$\therefore \dfrac{32}{24} = \dfrac{200}{x} + 1$
$\therefore \dfrac{32}{24} - 1 = \dfrac{200}{x}$
$\therefore \dfrac{8}{24} = \dfrac{200}{x}$
$\therefore x = \dfrac{200\times 24}{8}$
$\therefore x = 600$
Answer is $600$ days