Tag: rule of three

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Questions Related to rule of three

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

A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. when the car travels at the speed of 80 km/h it takes 

  1. one and half hour

  2. one hour

  3. two hour

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

Let the car takes x hours to reach a destination by travelling at the speed of 80 km/h. Then,

Speed (in km/hr) 60 80
Time (in hours) 2 x

Clearly, more the speed, less will be the time taken. So, it is a case of inverse proportion.
$ \therefore \,\,\, 60 \times 2 = 80 \times x  \Rightarrow x = \displaystyle \frac{60 \times 2}{80} = \frac{3}{2}$
Hence, the time taken will be $\displaystyle 1\frac{1}{2}$ hours.

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

Which is an example of inverse proportion?

  1. More amount of sweets, more total cost

  2. More length of cloth, more cost

  3. More expenditure, less saving

  4. More height of object, more length of its shadow
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

2 quantities say it be $x , y$ are said to be in proportion when the change in value of $x$ , leads to the equal change in value of $y$.

If $x$ increases and hence  $y$ decreases proportionally, it is called Inverse proportion i.e $x\propto\dfrac{1}{y}$
For example, In option C, if our expenses are more, then we are left with lesser savings from a fixed salary or income.
hence, Expenditure and savings are in inverse proportion.
So the answer is C

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

Which is example of inverse proportion?

  1. Length of edge of square & its area

  2. Speed and time taken

  3. Length of edge of square & its perimeter

  4. Quantity of pencils & total cost
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

2 quantities say it be $x , y$ are said to be in inverse proportion when the increse in value of $x$ , leads to the decrease in value of $y$.


we know that,
$speed = \dfrac{distance}{time}$

i.e., Speed is directly proportion to distance and at a fixed distance  inverse proportion to time.

Hence at fixed distance, if speed increses, time taken will decrease and vice versa. which is Option B

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

A car travels $40\ kms$ in $30$ mins. If the speed of bus remains same, how far can it travel in $3$ hrs?

  1. $120\ km$
  2. $80\ km$
  3. $240\ km$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
A car travels $40$ kms in $30$ mins
Let $x$ be the distance covered by a bus in $3$ hrs $=180$ mins
Then, $\dfrac {40}{30} = \dfrac {x}{180}$

$\Rightarrow x = \dfrac {40\times 180}{30} = 240\ km$.
Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

The number of workers increased the days to complete the work decreased."is example of 

  1. Inverse ratio

  2. Direct ratio

  3. Both of A and B

  4. none of above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Inverse proportion is a relation between two quantities such that one increases in proportion as the other decreases i.e. If $x$ increases as $y$ decreases, $x \alpha \dfrac{1}{y}$ 

In the given example, if the no. of workers are increased then the time required to do the job will decrease, likewise if no. of workers decrease, then time to do the same job will increase i.e. no. of workers and time to do job are inversely proportional to each other.
hence the answer is inverse proportion
So, the answer is option A.

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

Four angles of a quadrilateral are in the ratio $3:5:7:9$. The greatest angle is _________.

  1. $125^o$
  2. $75^o$
  3. $135^o$
  4. $120^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the angles of quadrilateral be $x,y,z,w.$
 
Given ,$x:y:z:w=3:5:7:9$

$x=3k$
$y=5k$
$z=7k$
$w=9k$

we k.n.t sum of angles of a quadrilateral is $360^{\circ }$
$x+y+z+w=3k+5k+7k+9k=360^{\circ }$
$\Rightarrow 24k=360^{\circ }$
$\Rightarrow k=\dfrac{360^{\circ }}{24}=15^{\circ }$

Greatest angle is $w=9k=9(15^{\circ })=135^{\circ }$
Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

A stone is dropped into a well and the report of the stone striking the bottom is heard $7.7$ seconds after it is dropped. Assume that the stone falls $16t^2m$ in t seconds and that the velocity of sound is $1,120$  per second. The depth of the well is:

  1. $784$m
  2. $342$m
  3. $1568$m
  4. $156.8$m

  5. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the distance d travelled by the stone and the sound is the same,

 $d = r _1t _1 = r _2t _2$.
 $\therefore$ The times of travel are inversely proportional to the rates of fail: 
$r _1/r _2 = t _2/t _1$,
$\therefore \dfrac{16t^2/t}{1120} = \dfrac{7.7-t}{t}; $
 $\therefore t = 7 (seconds);$
$ \therefore 16t^2 = 16\times 7^2 = 784 (metre)$.

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

A farmer has enough food to feed $28$ animals in his cattle for 9 days. How long would the food last if there were $8$ more animals in his cattle ?

  1. $5$
  2. $7$
  3. $10$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
let say each animal eat $x$ amount of food per day
$\rightarrow$ Amount of food eaten by $28$ animal for $1$ day
$=28 \times x$
$\rightarrow$ Amount of food required for $28$ animal for $9$ days
$=28 x \times 9$
$=(28 \times 9)x \ 252x$
$\therefore$ The farmer has $252x$ amount of food.
now, the number if animal $=28+8=36$.
$\boxed{No. of\ days\ the\ food\ will\ last = \dfrac{amount\ of\ food}{food\ required\ for\ 1\ day}}........1$
food required for $1$ day $=(no.of\ animals) \times x$
food requires for $1$ day $=36x $ (put\ this\ in\ $1$)
No. o days food will last $=\dfrac{252x}{36x}= \dfrac{252}{36}=7$
$\boxed{\because The\ food\ last\ for\ 7\ days\ if\ 8\ animals\ are\ added}$  

































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

Ten men, working for 6 days of 10 hours each, finish $ \dfrac {5}{21} $ of a piece of work. How many men working at the same rate and for the same number of hours each day, will be required to complete the remaining work in 8 days?

  1. 24

  2. 26

  3. 25

  4. 21
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lets first find the number of working hours required to complete $\dfrac { 5 }{ 21 }$ of the work.
M = number of men
D = number of days
H = number of hours worked per day
N = work done
MDH = N
10$\times $6$\times $10 = $\dfrac { 5 }{ 21 }$
600 hours to complete $\dfrac { 5 }{ 21 }$ of work
Let the total number of hours required to complete the work be $x$ then
$x$ = $\dfrac { 5 }{ 21 }$ $\div $600
   = 600$\times $$\dfrac { 21 }{ 5
 }$
$x$   = 2520 hours
so the remaining work is $x$$-$  $\dfrac { 5 }{ 21 }$
               = $\dfrac {16 }{ 21 }$ $x$

               =$\dfrac {16 }{ 21 }$$\times $2520
               = 1920 hours required to complete remaining $\dfrac {16 }{ 21 }$ of the work
 now the equation we get is
MDH = N
MDH = 1920
M $\times $ 8$\times $10 = 1920
M =  $\dfrac { 1920 }{ 80 } $
M = 24
 Ans. 24 men