Tag: rule of three

Quizzes (3) Questions (59)

Questions Related to rule of three

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

If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day ?

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the required number of days be x.
 Then,

Less pumps, More days (Indirect Proportion)


Less water, Less days (Direct Proportion)


More hours / day, Less days (Indirect Proportion)
 Pumps 8 : 9


Weight 1085 : 868
 Hours/day 9 : 7 :: 10 : x
$ (8 \times  1085 \times  9 \times  x) = (9 \times  868 \times  7 \times  10)$
$ x = (9 \times  868 \times  7 \times  10)/(8 \times  1085 \times  9)$
$ x=7 $
Answer (B) 7

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

If $a : b = 5 : 9$ and $b : c = 4 : 7$ find $a : b : c$

  1. $5:9:\dfrac{63}{4}$
  2. $20:63:36$
  3. $4:36:63$
  4. $20:36:63$
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

Given, $a : b = 5 : 9 $ and $b : c = 4 : 7$ $=$ $\displaystyle \left ( 4\times

\frac{9}{4} \right ):\left ( 7\times \frac{9}{4} \right

)=9:\frac{63}{4}$
$\displaystyle \Rightarrow a:b:c=5:9:\frac{63}{4}=20:36:63$

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

Cost of 10 mangoes is Rs. 100 The cost of 18 mangoes is__ 

  1. Rs. 18

  2. Rs. 108

  3. Rs. 200

  4. Rs. 180
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cost of mangoes is directly proportional to the number of mangoes bought.

So, if $ 10 $ mangoes costs $ Rs\  100 $, then $ 1 $ mango will cost $ Rs \dfrac{ 100 }{10}  = Rs  10 $

And $ 18 $ mangoes will cost $ 18 \times Rs \dfrac{ 100 }{10}  = Rs 180 $

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

A bus travels 120 km in 4 hrs  The distance that can be travelled by the bus in 6 hrs is__

  1. 18 km

  2. 140 km

  3. 180 km

  4. 120 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distance travelled is directly proportional to the number of hours travelled.

So, if  in $ 4 $ hours, $ 120\ km $ is travelled then in $ 1 $ hour  distance travelled is $  \dfrac{ 120 }{4}\ km $  

And in  $ 6 $ hours, distance travelled is  $ 6 \times \dfrac{ 120 }{4}  = 180\ km $

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.