Tag: rule of three

Questions Related to rule of three

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

  $a$ $2$ $3$ $4$ $5$
  $b$  $14$ $21$ $x$ $35$
maths direct proportion and inverse proportion rule of three types of proportions direct proportion

  1. $16$

  2. $25$

  3. $27$

  4. $28$

Show answer
Correct Option: D
Explanation:

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

$a$ and $b$ are in ............ proportion

$a$ $3$ $7$ $10$ $11$
$b$ $9$ $21$ $30$ $33$
maths direct proportion and inverse proportion rule of three types of proportions direct proportion

  1. direct

  2. indirect

  3. both

  4. none

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Correct Option: A
Explanation:

$\dfrac {a}{b} = \dfrac {3}{9} = \dfrac {7}{21} = \dfrac {10}{30} = \dfrac {11}{33} = \dfrac {1}{3} = k$
$\therefore a$ and $b$ are in direct proportion.

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

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

  1. Direct

  2. Inverse

  3. No proportionality

  4. Can't be determinal

Show answer
Correct Option: A
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
$\Rightarrow a\propto c$

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.

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

  1. $50$

  2. $500$

  3. $1000$

  4. $1600$

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Correct Option: B

$A, B$ 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?

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

  1. $12$

  2. $9$

  3. $15$

  4. $18$

Show answer
Correct Option: A
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.

If $4$ men earn Rs $360$ in one day, then how much does a man earn in one day?

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

  1. $90$

  2. $30$

  3. $120$

  4. $60$

Show answer
Correct Option: A
Explanation:

Earning of $4$ men $=$ Rs $360$ per day
Earning of $1$ man $=$ Rs $\dfrac{360}{4}$ per day

                             $=$ Rs $90$ per day

Which of the following is the example of direct proportion?

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

Show answer
Correct Option: A
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.

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

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

  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. $1680$

Show answer
Correct Option: B
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$=Rs. \left(\displaystyle\frac{5040}{4}\right)=Rs. 1260$.

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

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

  1. $5, 14$

  2. $14, 5$

  3. $8, 10$

  4. $10, 8$

Show answer
Correct Option: A
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
$20:28=10:y\Rightarrow 20\times y=28\times 10$
$\Rightarrow y=\displaystyle\frac{10\times 28}{20}=14$.