Tag: direct proportion

Questions Related to direct proportion

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

If $a:b=c:d$ then how many of the following statements are true?

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

  1. $c(a+b)=a(c+d)$

  2. $d(a-b)=b(c-d)$

  3. $(a^{2}+b^{2})(ac-bd)=(a^{2}-b^{2})(ac+bd)$

  4. $(a^{2}-b^{2})(ad-bc)=(a^{2}+b^{2})(ac-bd)$

Show answer
Correct Option: A
Explanation:

$\dfrac{a}{b}=\dfrac{c}{d}$
$\dfrac{b}{a}=\dfrac{d}{c}$

$\left(1+\dfrac{b}{a}\right)=\left(1+\dfrac{d}{c}\right)$
$\dfrac{(a+b)}{a}=\dfrac{(c+d)}{c}$
$c(a+b)=a(c+d)$

Mark the correct alternative of the following.
Two numbers are in the ration $3 : 5$ and their sum is $96$. The larger number is?

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

  1. $36$

  2. $42$

  3. $60$

  4. $70$

Show answer
Correct Option: C
Explanation:

Given two numbers are  in the ratio $3:5$.

Let the numbers are $3x$ and $5x$.
Then according to the problem we get,
$3x+5x=96$
or, $8x=96$
or, $x=12$.
So the largest number is $12\times 5=60$.

If $4$ men or $6$ women earn Rs $360$ in one day, then find how much less does a woman earn in one day than men.

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

  1. Rs $20$

  2. Rs $30$

  3. Rs $40$

  4. Rs $35$

Show answer
Correct Option: B
Explanation:

$6$ women earn = Rs $360$ $/day$


$\therefore 1$ woman earns = Rs $\dfrac{360}{6}$ $/day$


                             = Rs $60$ $/day$.
$4$ men earn = Rs $360$ $/day$

$\therefore 1$ man earns = Rs $\dfrac{360}{4}$ $/day$

                             = Rs $90$ $/day$.
$\therefore$ women earn Rs 30 less than man

Eight oranges can be bought for Rs $10.40$, then how many more oranges can be bought for Rs $16.90$?

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

  1. $5$ oranges

  2. $3$ oranges

  3. $7$ oranges

  4. $2$ oranges

Show answer
Correct Option: A
Explanation:

Let $x$ oranges  be bought for Rs.$ 16.90.$


Given, eight oranges are bought for Rs.$ 10.40.$

Then, $\dfrac{8}{x}=\dfrac{10.40}{16.90}$

$\Longrightarrow x=\dfrac{16.90\times 8}{10.40}=13$

Then, $(13-8)=5$ more oranges can be bought.