Tag: rule of three

Questions Related to rule of three

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)

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.

Show answer
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. $300$

Show answer
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

A man eats $200:g$ of rice a day and he has enough rice to last him for $35$ days. How long would the stock of rice last him if he were to eat $250:g$ rice a day.

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

  1. $\;42$

  2. $\;21$

  3. $\;28$

  4. $\;49$

Show answer
Correct Option: C
Explanation:

Man eat $ 200$ g rice in a day then he  has $35\times 200=7000  g $ rice for  $35$  days
But if he eat  $250$  g rice in a day
Then $7000$  g rice is enough for $\dfrac{7000}{250}=28  \ days$

The price of $357$ mangoes is $Rs. 1517.25.$ What will be the approximate price of $49$ dozens of such mangoes?

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

  1. $Rs. 3000$

  2. $Rs. 3500$

  3. $Rs. 4000$

  4. $Rs. 2500$

Show answer
Correct Option: D
Explanation:

Let the required price be Rs. x. Then, more mangoes, more price
$\therefore$ $357 : (49 \times 12) :: 1517.25 : x$
$\Rightarrow 357x = (49 \times 12 \times 1517.25)$
$\Rightarrow\, x\, =\, \displaystyle \frac{(49\, \times\, 12\, \times\, 1517.25)}{357}\, =\, 2499$
Hence, the approximate price is Rs. 2500

On a scale of map, $0.6$ cm represents $ 6.6$km. If the distance between the points on the map is  $80.5$  cm, the actualdistance between these points is

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

  1. $9$ km

  2. $72.5$ km

  3. $190.75$ km

  4. $885.5$ km

Show answer
Correct Option: D
Explanation:

Let the actural distance be x km. Then, more distance on the map, more is the actual distance. 
$\therefore$ 0.6 : 80.5 :: 6.6 : x
$\Rightarrow\, 0.6x\, =\, 80.5\, \times\, 6.6$
$\Rightarrow\, x\, =\, \displaystyle \frac{80.5\, \times\, 6.6}{0.6}\, \Rightarrow\, x\, =\, 885.5$

If x & y are in direct proportion and if $x=20$ at proportionality constant $=4$, find y.

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

  1. $2$

  2. $3$

  3. $4$

  4. $5$

Show answer
Correct Option: D
Explanation:

$\dfrac{x}{y}=K\;\Rightarrow\;\dfrac{20}{y}=4\;\Rightarrow\;y=\dfrac{20}{4}=5$

Which is an example of direct proportion?

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

  1. More working hours, more earning

  2. More speed of car, less time taken

  3. More no. of workers, less time taken

  4. Less the age of person, more active he is

Show answer
Correct Option: A
Explanation:

2 quantities say it be $x , y$ are said to be in proportion when the change in value of $x$ , leads to the equal change in value of $y$.

If $x$ increases, $y$ increases proportionally, it is called Direct proportion
i.e if a person works more time, he will earn more which is option A.
in other option, are the examples of inverse proportion
so the answer is Option A 

Observe the values and find the quantities which are in direct proportion
$ \begin{equation}x : \;\;[4\;\;6\;\;8\;\;10] \ y : \;\;[2\;\;3\;\;4\;\;\;5] \ z : \;\;[1\;\;2\;\;3\;\;\;4]\end{equation}$

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

  1. x & y

  2. y & z

  3. x & z

  4. None of these

Show answer
Correct Option: A
Explanation:

By definition of direct proportion,

$a \  \alpha \  b$ i.e. $a = Kb$ where $K$ is constant of proportionality
$\therefore \dfrac{a}{b} = K$  ........ equation $1$

From given example, consider
$\dfrac{x}{y} =\dfrac{4}{2} = \dfrac{6}{3} = \dfrac{8}{4} = \dfrac{10}{5} = 2$

where as
$\dfrac{x}{z} = \dfrac{4}{1}\neq\dfrac{6}{2}\neq\dfrac{8}{3}\neq\dfrac{10}{4}$

$\therefore$ $x$ and $y$ obey the equation $1$

Hence $x$ and $y$ are in inverse proportion.
Answer is A