Free Ratio and Proportion Subjective Test 02 Practice Test - 6th grade 

Solution: 1 Mark

Since $x:32$ and $4:16$ are equivalent ratios,

we can write, $\frac{x}{32}=\frac{4}{16}$

$\Rightarrow x=\frac{4\times 32}{16}$

Solving for x we get:

$x=8$

Each Option: 1 Mark

(a) $2hrs=60\times 2=120$ minutes   (1 hr = 60 minute)
Ratio of 20 minutes to 2 hrs = 20:120 =1:6
[ Remember that for taking ratio unit of both quantities should be same ]

(b) $5:4::125:x\Rightarrow \frac{5}{4}=\frac{125}{x}$

$\Rightarrow \frac{5}{4}=\frac{125}{x}$
$\Rightarrow \frac{4}{5}=\frac{x}{125}$

$\Rightarrow x=\frac{125\times 4}{5}=25\times 4$

$\Rightarrow x=100$

Each option: 1 Mark

Total number of students in volleyball= 45

Total number of students in football  = 25

Total number of students in tennis = 100 - (45 + 25) = 30

(a) The ratio of number of students in Volleyball to number of students in football = 45 : 25 = 9 : 5

(b) The ratio of number of students in Volleyball to number of students in tennis = 45 : 30 = 3 : 2

Steps: 2 Marks
Answer: 1 Mark

Area of first circle
$A_1=\pi r^2=\pi 5^2$

Area of second circle
$A_2=\pi r^2=\pi 3^2$

Ratio of the area of two circles:
$\pi 5^2:\pi 3^2=25:9$

Steps: 2 Marks
Answer: 1 Mark

Number of runs made by Anish in 6 overs
 = 42

Number of runs made by Anup in 7 overs
=  63

Number of runs made by Anish in 1 overs
= $\frac{42}{6}$ = 7

Number of runs made by Anup in 1 overs
= $\frac{63}{7}$ = 9

Therefore, Anup made more runs per over.

Ratio of their runs made

$\frac{Anish}{Anup}=\frac{42}{63}=\frac{2}{3}\Rightarrow 2:3$

Steps: 2 Marks
Answer: 1 Mark

Marks scored by Aamir = 54

Marks scored by Usha = 100 - 34 = 66

The ratio of the marks of Aamir to Usha = 54 : 66 = 9 : 11

Marks scored by Preeti = 72

Let the marks scored by Kunal be $x$.

$\therefore 72:x=9:11$
$\Rightarrow \frac{72}{x}=\frac{9}{11}$
$\Rightarrow \frac{x}{72}=\frac{11}{9}$

$\Rightarrow x=\frac{72\times 11}{9}=8\times 11$

$\Rightarrow x=88$

$\therefore$ Marks obtained by Kunal is $88$.

Observing correct number of figures: 1 Mark each
Correct ratio in simplest form: 1 Mark each

a) Number of triangles = 6
    Number of stars = 4
$\Rightarrow$Ratio of the number of triangles to the number of stars = 6 : 4 = 3 : 2

b)  Number of rhombi =6 
     Total number of figures = 16
$\Rightarrow$ Ratio of the number of rhombus to the total number of figures
= 6 : 16 = 3 : 8

Steps: 3 Marks
Answer: 1 Mark

Let the speed of Raj and Alisha be S1 and S2 respectively.

The ratio of the distance of raj's house to the school and Alisha's house to the school $=\frac{D_1}{D_2}=\frac{13}{17}$

Since the time is same, time = T

The ratio of walking speed of Raj and Alisha
$=\frac{S_1}{S_2}$

$\frac{S_1}{S_2}=\frac{D_1.T}{D_2.T}=\frac{13}{17}$

Ratio of walking speed of Raj and Alisha is 13 : 17

Concept: 1 Mark
Application: 1 Mark
Steps: 1 Mark
Solution: 1 Mark

Let x and y be the weight of Meenakshi and Ankur has respectively.

The ratio of the weights of Meenakshi to Ankur  = 13:15

After exercising, ratio of the weights of Meenakshi to Ankur = x :( y-5) = 13:14

Comparing both $\frac{x}{y}$ =  $\frac{13}{15}$  and  $\frac{x}{y-5}$  =  $\frac{13}{14}$ we get,

$\Rightarrow 13y=15x..............\left(i\right)$ and
 $14x=13(y-5)$
$\Rightarrow 14x=13y-\mathrm{65............}\left(ii\right)$

Substituting the value of (i) in (ii) we get,
$\Rightarrow 14x=15x-65$.
$x=65$

Substitute the value of x in (i)
$\Rightarrow 13y=15\times 65$
$y=15\times 5=75$

But Ankur lost 5 kg 

$\therefore$ Ankur's present weight is $(y-5)=(75-5)=70kg$

Ravi' Share: 1 Mark
Rani's Share: 1 Mark
Steps: 2 Marks

Let the share of Ravi and Rani be x and y respectively.

Total Profit = Rs. 40,000

Ratio of investment of Ravi to Rani = 2:3
Total parts of profit = 2+3 =5 
 

$x=\frac{2}{5}\times 40000$ = Rs. 16000

$y=\frac{3}{5}\times 40000$ = Rs. 24000

Share of Ravi in Profit is Rs. 16,000

Share of Rani in Profit is Rs. 24,000