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

### Question 1

If x:32 and 4:16 are equivalent ratio, then find the value of x. [1 MARK]

#### SOLUTION

Solution :Solution: 1 Mark

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

we can write, x32=416

⇒x=4×3216

Solving for x we get:

x=8

### Question 2

(a) The ratio of 20 minutes to 2 hrs.

(b) Find x if 5:4::125:x

[2 MARKS]

#### SOLUTION

Solution :Each Option: 1 Mark

(a) 2 hrs=60×2=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⇒54=125x

⇒54=125x

⇒45=x125

⇒x=125×45=25×4

⇒x=100

### Question 3

In a class, there are 100 students, 45 students have chosen volleyball and 25 students have chosen football and the remaining have chosen tennis. Find:

(a) The ratio of the number of students in volleyball to the number of students in football and

(b) The ratio of students in volleyball to that in tennis. [2 MARKS]

#### SOLUTION

Solution :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

### Question 4

Find the ratio of areas of two circles if they have a radius as 5 and 3 respectively. [3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 1 Mark

Area of first circle

A1=πr2=π52

Area of second circle

A2=πr2=π32

Ratio of the area of two circles:

π52:π32=25:9

### Question 5

Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over and what is the ratio of their total runs made? [3 MARKS]

#### SOLUTION

Solution :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

= 426 = 7

Number of runs made by Anup in 1 overs

= 637 = 9

Therefore, Anup made more runs per over.

Ratio of their runs made

AnishAnup=4263=23⇒2:3

### Question 6

In an examination which has questions of 100 marks, Aamir scores 54 marks while Usha loses 34 marks in her paper. The ratio of the marks of Aamir to that of Usha is same as that of the marks obtained by Preeti and Kunal. If Preeti scored 72 marks, how much did Kunal score? [3 MARKS]

#### SOLUTION

Solution :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.

∴72:x=9:11

⇒72x=911

⇒x72=119

⇒x=72×119=8×11

⇒x=88

∴ Marks obtained by Kunal is 88.

### Question 7

Look at the figure and find the ratio of :

(a) The number of triangles to the number of stars in the rectangle.

(b) The number of rhombus to the total number of figures in the rectangle. [4 MARKS]

#### SOLUTION

Solution :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

⇒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

⇒ Ratio of the number of rhombus to the total number of figures

= 6 : 16 = 3 : 8

### Question 8

Raj and Alisha start walking to school at the same time every morning. The ratio of the distance of Raj's house to the school and Alisha's house to the school is 13 : 17. If they both reach school at the same time, then the ratio of the walking speed of Raj and Alisha is? [4 MARKS]

#### SOLUTION

Solution :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 =D1D2=1317

Since the time is same, time = T

The ratio of walking speed of Raj and Alisha

=S1S2S1S2=D1.TD2.T=1317

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

### Question 9

The ratio of the weights of Meenakshi to that of her friend Ankur is 13:15. Ankur now starts to exercise daily and loses 5 kg, and now the ratio of their weights is 13:14. How much does Ankur weigh now?

#### SOLUTION

Solution :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 xy = 1315 and xy−5 = 1314 we get,

⇒13y=15x..............(i) and

14x=13(y−5)

⇒14x=13y−65............(ii)

Substituting the value of (i) in (ii) we get,

⇒14x=15x−65.

x=65

Substitute the value of x in (i)

⇒13y=15×65

y=15×5=75

But Ankur lost 5 kg

∴ Ankur's present weight is (y−5)=(75−5)=70kg

### Question 10

Ravi and Rani started a business and invested money in the ratio 2 : 3. After one year the total profit was Rs 40,000. What are the shares of Ravi and Rani in the profit? [4 MARKS]

#### SOLUTION

Solution :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=25×40000 = Rs. 16000

y=35×40000 = Rs. 24000

Share of Ravi in Profit is Rs. 16,000

Share of Rani in Profit is Rs. 24,000