Tag: direct proportion and inverse proportion

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Questions Related to direct proportion and inverse proportion

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

Find the value of $x$ if  $a$ and $ b$  are in direct proportion

  $a$ $2$ $3$ $4$ $5$
  $b$  $14$ $21$ $x$ $35$
  1. $16$
  2. $25$
  3. $27$
  4. $28$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$a$ and $b$ are in direct proportion
$\therefore \dfrac {a}{b} = k = \dfrac {2}{14} = \dfrac {3}{21} = \dfrac {1}{7}$
$\therefore \dfrac {4}{x} = \dfrac {1}{7} \Rightarrow x = 28$.

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

If  $a$  is inversely proportional to  $b $ and  $b$  is inversely proportional to  $c $ then what is proportionality between  $a $ and  $c$?

  1. Direct

  2. Inverse

  3. No proportionality

  4. Can't be determinal
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$a\propto \dfrac {1}{b} \Rightarrow a = \dfrac {k _{1}}{b}; k _{1}$ is a constant
$b\propto \dfrac {1}{c} \Rightarrow b = \dfrac {K _{2}}{c}; k _{2}$ is a constant
$\Rightarrow a = \dfrac {k _{1}c}{k _{2}} = k _{3}c; k _{3} = \dfrac {k _{1}}{k _{2}}$ is another constant
$\Rightarrow a\propto c$

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

The correct dosage of adult over-the-counter medicine a child can receive is given by a formula by Clark. The child's weight, in pounds, is divided by $150$, and the result is multi pounds lied by the adult dose of the medicine. A mother need to give her daughter acetaminophen, which has an adult dose of $ 1000$ milligrams. She does not know her daughter's exact weight, but she knows the weight is  and between $75 $ and $90 $pounds. Find the range of correct dosage, d, in milligrams of acetaminophen the daughter could receive.

  1. $50$
  2. $500$
  3. $1000$
  4. $1600$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Clark's formula is (weight/150) * adult dose. For 75 lbs: (75/150) * 1000 = 500 mg. For 90 lbs: (90/150) * 1000 = 600 mg. The range is 500 to 600 mg, making 500 the only viable option provided.

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

$A, B$ and $C$ can finish a job working alone in $72, 24$ and $36$ days respectively. In how many days they can finish the job if they worked together?

  1. $12$
  2. $9$
  3. $15$
  4. $18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the total work be $72$ units (LCM on $72, 24$ and $36$).


$A, B$ and $C's$ one day work is $1, 3$ and $2$ units respectively.

Required number of days $= \dfrac {72}{6} = 12$.


Alternate method
$(A+B+C)'s$ one day work =$\dfrac{1}{72}+\dfrac{1}{24}+\dfrac{1}{36}$

$=\dfrac{1+2+3}{72}=\dfrac{6}{72}$

Number of days required $= \dfrac {72}{6} = 12$ days to finish the work when 3 of them work together.

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

Which of the following is the example of direct proportion?

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

  2. Speed goes up ,travel times goes down.

  3. More the number of men lesser the time taken to complete it.

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

Directly proportional: as one amount increases, 
another amount increases at the same rate.
Hence, in option A when number of mangoes in a bag increases,then the weight of the bag also increases.

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

Share of A, B and C respectively, are ____________, if Rs. $5460$ is divided in $\displaystyle\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$.

  1. Rs. $1680$, Rs. $2520$, Rs. $1260$
  2. Rs. $2520$, Rs. $1680$, Rs. $1260$
  3. Rs. $1260$, Rs. $2100$, Rs. $2520$
  4. Rs. $2520$, Rs. $1260$, Rs. $1680$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let A's share $=Rs.\left(\displaystyle\frac{x}{2}\right)$
B's share $=Rs.\left(\displaystyle\frac{x}{3}\right)$
And C's share $=Rs.\left(\displaystyle\frac{x}{4}\right)$
According to equation,
$\displaystyle\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=5460$
$\Rightarrow \displaystyle\frac{6x+4x+3x}{12}=5460$
$\Rightarrow 13x=5460\times 12\Rightarrow x=\displaystyle \frac{5460\times 12}{13}=5040$
$\therefore$ A's share $=Rs. \left(\displaystyle\frac{5040}{2}\right)=Rs. 2520$
B's share$=Rs.\left(\displaystyle\frac{5040}{3}\right)=Rs. 1680$
And C's share$=Rs. \left(\displaystyle\frac{5040}{4}\right)=Rs. 1260$.
Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

If $20: 28= x:7=10:y$.
The values of $x$ and $y$ in the box respectively are __________.

  1. $5, 14$
  2. $14, 5$
  3. $8, 10$
  4. $10, 8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
We have, $20:28=x:7=10:y$
Taking first two ratios, we have
$20:28=x:7$
$\Rightarrow 20\times 7=x\times 28$
$\Rightarrow x=\displaystyle\frac{20\times 7}{28}=5$
Again taking last and first ratio, we get
$20:28=10:y\Rightarrow 20\times y=28\times 10$
$\Rightarrow y=\displaystyle\frac{10\times 28}{20}=14$.