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

If y is directly proportional to x & when $x=2$ & $y=4$, what is constant of proportionality?

  1. $1$
  2. $3$
  3. $5$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By definition of proportionality,

If $y$ is directly proportional to $x$,
$y$ $ \alpha$ $ x$
$\therefore y = Kx$     .......Equation $1$
where $K$ is constant of proprtionality
Now,
Given that $x = 2 , y = 4$
putting the above values in Equation $1$ we get, 
$4 = K\times 2$
$\therefore K = 2$

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

A drum of kerosene oil is $\dfrac {3}{4}$ full. When $30$ litres of oil are drawn from it, it is $\dfrac {7}{12}$ full. Find the capacity of the drum ?

  1. $120$ litres
  2. $140$ litres
  3. $180$ litres
  4. $240$ litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let capacity of drum  $=  x$ litres
Initially, drum was $\dfrac {3x}{4}$ part filled
$30$ litres oil drawn then it become, $\dfrac {7x}{12}$ part.
Now, according to question,
$\dfrac {3x}{4} - \dfrac {7x}{12} = 30$
$\Rightarrow \dfrac {(9x - 7x)}{12} = 30$
$\Rightarrow 2x = 360$
$\Rightarrow x = 180$ litres

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

If x & y are in direct proportion then find the value of a
$\begin{equation}x\;\;2\;\;3\;\;5\;\;\;7 \ y\;\;4\;\;6\;\;a\;\;14\end{equation}$

  1. $8$
  2. $10$
  3. $15$
  4. $20$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{x}{y}=K$ (Direct proportion)


$\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{5}{a}=\dfrac{7}{14}=K\;\Rightarrow\;K=\dfrac{1}{2}=\dfrac{5}{a}\;\Rightarrow\;a=10$

Thus option B is the correct answer.

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.