# Free Ratio and Proportion Subjective Test 01 Practice Test - 6th grade

### Question 1

Express as simple ratio: [1 MARK]

312:213

#### SOLUTION

Solution :Solution: 1 Mark

312:213=72:73

=72×37=32=3:2

### Question 2

The length and breadth of a rectangular field are in the ratio 4 : 5. If the length is 20m, find the breadth of the field. [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Solution: 1 Mark

Length(l):Breadth (b)=4:5

⇒lb=45

Given: l=20m

⇒20b=45

⇒b20=54

⇒b=5×204

b=5×5=25

∴Breadth of the field=25m

### Question 3

Find the value of x if x:4 and 6:8 are equivalent ratios. [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Answer: 1 Mark

If x:4 and 6:8 are equivalent ratios. Then

x:4=6:8⇒x4=68

⇒x=6×48=3

∴x=3

### Question 4

Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find ratio of [3 MARKS]

a) Number of students liking football to number of students liking tennis

b) The number of students liking cricket to the total number of students

#### SOLUTION

Solution :Each Option: 1.5 Mark

Number of students liking tennis =30−(6+12)=30−18=12

a) Ratio of number of students liking football to number of students liking tennis

=6:12=1:2b) Ratio of number of students liking cricket to total number of students

=12:30=2:5Hence,

Ratio of number of students liking football to number of students liking tennis =1:2

Ratio of number of students liking cricket to total number of students =2:5

### Question 5

For the last 10 days, Kareem spent the same amount every day and has spent a total of Rs.230. What is the ratio of his expenditure? (i.e. number of days to the amount spent on that day) If he has Rs.345 left with him, in how many more days will he finish this amount? [3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 1 Mark

Kareem's expense for 10 days =Rs.230

Kareem's expense for 1 day =23010=Rs.23

Ratio of Kareem's expenditure =1:23

Total amount left with Kareem =Rs.345

Number of days to finish Rs.345

⇒34523=15 days

### Question 6

There are 20 girls and 15 boys in a class. [3 MARKS]

a) What is the ratio of the number of boys to the number of girls?

b) What is the ratio of the number of girls to the total number of students in the class?

c) What is the ratio of the number of boys to the total number of students in the class?

#### SOLUTION

Solution :Each option: 1 Mark

Total number of students in class=20+15=35

(a) Ratio of number of boys to the number of girls

=15:20=1520=34

Hence, ratio of number of boys to the number of girls is 3:4

(b) Ratio of number of girls to the total number of students

=20:35=2035=47

Ratio of number of girls to the total number of students is =4:7

(c) Ratio of number of boys to the total number of students

=15:35=1535=37

Ratio of number of boys to the total number of students is =3:7

### Question 7

How can 20 pens be divided between Sujay and Ram in the ratio of 4:1? [4 MARKS]

#### SOLUTION

Solution :Steps: 3 Marks

Answer: 1 Mark

Ratio between Sujay and Ram = 4:1

Total value = 4+1 = 5

Therefore, Sujay’s part of total pencils = 45

Ram’s part of total pencils = 15

Thus, Pencils with Sujay

= 45×20=16

Pencils with Ram = 15×20=4

### Question 8

Cost of 6kg of wheat is Rs.72 and cost of 5kg of rice is Rs.450 [4 MARKS]

(a) What will be the cost of 8kg of wheat?

(b) What will be the cost of 1kg of rice?

(c) What is the ratio of the price of 1kg of rice to 1kg of wheat?

#### SOLUTION

Solution :a Part: 1 Mark

b Part: 1 Mark

c Part: 2 Marks

(a) Cost of 6 kg of wheat = Rs 72

Cost of 1 kg of wheat =726=Rs.12

Cost of 8 kg of wheat =12×8

= Rs.96

(b) Cost of 5 kg of rice = Rs 450

Cost of 1 kg of rice =4505

= Rs.90

(c) Ratio of price of 1kg of rice to 1kg of wheat

⇒9012=152=15:2

### Question 9

Sonia and Surjeet started a competition to see who can collect the most number of stamps. At the end of one month, the ratio of the stamps Sonia had to those that Surjeet had was 89 : 93. If Surjeet has 2325 stamps. How many stamps does Sonia have? [4 MARKS]

#### SOLUTION

Solution :Steps: 3 Marks

Answer: 1 Mark

Let x and y be the number of stamps Sonia and Surjeet have respectively.

At the end of one month,

Ratio of the stamps of Sonia to Surjeet

= x : y = 89 : 93

xy=8993

x=y.8993

Given: y = 2325

x=2325×8993

x=2325×8993=2225Hence Sonia has 2225 stamps.

### Question 10

Neha's toy car can travel 288 meters in a minute while Vendetta's toy car can travel 24.48 kilometres in an hour. The ratio of the speed of the cars belonging to Neha and Vendetta is: [4 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 2 Marks

Distance travelled by Neha's toy car in a minute = 288m

Speed of Neha's toy car = 288 m/min

Distance travelled by Vendetta's toy car in an hour (60 minutes) = 24.48km= 24480m (⇒1km = 1000m)

Distance travelled by Vendetta's toy car in a minute= 24480÷60 = 408 m

Speed of Vendetta's toy car=408 m/min

The ratio of the speed of the cars belonging to Neha and Vendetta =288 : 408 =12 : 17