Tag: maths

Questions Related to maths

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

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

  1. $1$

  2. $3$

  3. $5$

  4. $2$

Show answer
Correct Option: D
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, 
$4 = K\times 2$
$\therefore K = 2$

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 ?

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

  1. $120$ litres

  2. $140$ litres

  3. $180$ litres

  4. $240$ litres

Show answer
Correct Option: C
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

Which of the following $a$ & $b$ are in direct proportion?

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

  1. $a=\dfrac{2}{b}$

  2. $a=2b$

  3. $a=b^3$

  4. $a=\dfrac{1}{b^2}$

Show answer
Correct Option: B
Explanation:
For proportion $a:b=c:d$
$a=2b$
$\Rightarrow a:b=2:1$

The cost of $2$ meter cloth is $10$. Find the cost of $100\ m$ cloth.

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

  1. $400$

  2. $500$

  3. $1000$

  4. $1500$

Show answer
Correct Option: B
Explanation:

Cost of cloth is directly proportional to its length.
$10 = 2\times k \Rightarrow k = 5$    , where k is the cost of cloth per meter
$\therefore$ Cost of $100\ m$ cloth $=5\times 100 = 500$.

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

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

  1. $8$

  2. $10$

  3. $15$

  4. $20$

Show answer
Correct Option: B
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.

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

Show answer
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. $1600$

Show answer
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.