Tag: direct proportion

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Questions Related to direct proportion

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

  1. $\;42$
  2. $\;21$
  3. $\;28$
  4. $\;49$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\dfrac{7000}{250}=28  \ days$

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

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

  1. $Rs. 3000$
  2. $Rs. 3500$
  3. $Rs. 4000$
  4. $Rs. 2500$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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

  1. $9$ km
  2. $72.5$ km
  3. $190.75$ km
  4. $885.5$ km
Reveal answer Fill a bubble to check yourself
D Correct answer
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
$\Rightarrow\, 0.6x\, =\, 80.5\, \times\, 6.6$
$\Rightarrow\, x\, =\, \displaystyle \frac{80.5\, \times\, 6.6}{0.6}\, \Rightarrow\, x\, =\, 885.5$

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

Which is an example of 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
Reveal answer Fill a bubble to check yourself
A Correct answer
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 

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

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}$

  1. x & y

  2. y & z

  3. x & z

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  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. $(a^{2}-b^{2})(ad-bc)=(a^{2}+b^{2})(ac-bd)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

  1. $36$
  2. $42$
  3. $60$
  4. $70$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $12\times 5=60$.

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

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.

  1. Rs $20$
  2. Rs $30$
  3. Rs $40$
  4. Rs $35$
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  1. $5$ oranges
  2. $3$ oranges
  3. $7$ oranges
  4. $2$ oranges
Reveal answer Fill a bubble to check yourself
A Correct answer
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.