Free Direct and Inverse Proportions 01 Practice Test - 8th Grade 

Let the required number of days with 30 men working for 6 hours be x.
$\begin{array}{ccc}\text{Number of men}& 39& 30\\ \text{Number of hours}& 5& 6\\ \text{Number of days}& 12& x\end{array}$

Number of men, number of hours and number of days are inversely proportional and work done is constant in both the cases, hence

$\Rightarrow 39\times 12\times 5=30\times x\times 6x=\frac{39\times 12\times 5}{30\times 6}x=13\text{days}$

Given distance s is directly proportional to square of time t.

That is:
 $s=k.t^{2}20=4kk=5\text{So,}s=5t^{2}605=5t^2$

t = 11 seconds

Let the required number of machines be denoted by 'n' and number of days taken be 'd'.

As number of machines increases, the number of days required to make articles decreases, hence they are inversely proportional.

$n\times d$ = constant
$n_1\times d_1$ = $n_2\times d_2$

Using inverse proportion condition, 

 $\frac{42}{n}$ = $\frac{54}{63}$

$n=\frac{42\times 63}{54}$ 

n = 49

So, 49 machines are required.
Hence, the statement is false.

As animals increases, the number of days decreases. This is in inverse proportion.

Let the required number of days be t

20 x 6 = 30 x t

t = 4

So, the food will last for 4 days.

Given, the number of bottles can be filled by the machine in 6 hours = 480

Hence number of bottles it can fill in 1 hour = $\frac{480}{6}$= 80 bottles
Hence the number of bottles that can be filled in 2 days = 80 $\times$  2 $\times$ 24       ($\because$ Number of hours in a day = 24) 
= 3840 bottles

Given, the number of bottles that can be filled by the machine in 6 hours is 840.

Hence, the number of bottles it can fill in 1 hour
$=\frac{840}{6}$
= 140 bottles

Hence number of bottles that can be filled in 5 hours
$=140\times 5$
= 700 bottles 

Let h represents the height of the tower that casts 300 m long shadow.

$\frac{14}{h}=\frac{10}{300}$

10 x h = 14 x 300

h = 420 metres

As Raghu goes at same speed , $\frac{Distance}{Time}$ remains constant.

Assume that the distance covered in 4 hours be x.

10x = 4 x 60 x 2

$x=48km$.

Hence Raghu can reach city A in given time.

$\frac{Lengthofsquare}{Perimeterofsquare}=\frac{a}{4a}=\frac{1}{4}$
which is a constant.

$\frac{Lengthofsquare}{Areaofsquare}=\frac{a}{a^2}=\frac{1}{a}$
which is not constant. 

$\frac{Lengthofsquare}{Lengthofdiagonal}=\frac{1}{\sqrt{2}}$
which is constant.

Hence, length of a square is in direct proportion with its perimeter and diagonal.

When $x$ and $y$ are in direct proportion, we can write $\frac{x_1}{y_1}=\frac{x_2}{y_2}$

[$y_1,y_2$ are values of $y$ corresponding to the values $x_1,x_2$ of $x$ respectively] which gives $x_1{y}_2=x_2{y}_1$.