Grade 6 Ratio and Proportion In

ID : in-6-Ratio-and-Proportion [1]

Class 6 Ratio and Proportion For more such worksheets visit www.edugain.com

Answer the questions (1)

A public school in the city have 1170 girls among 2160 students. What is the ratio of boys to girls in the school?

(2)

Iqbal's grandparents live 108 km away from his house. When Iqbal wants to visit them, he travels 24 km of the distance through a bus and the rest by train. What is the ratio of the distance Iqbal travels by bus to the distance he travels by train?

(3)

In a T20 cricket match, the first team has made 95 runs. If the second team has made 42 runs, what is the ratio of the runs they have made to the runs they need to win the match?

(4)

What are the extremes of the proportion 16:32::112:224?

(5)

In a warehouse, the workers start their work daily at 07:15 AM and end at 04:30 PM. They get a break of 25 minutes to have lunch, and two coffee breaks of 10 minutes each. What is the simplest form of ratio of the time they spend working to the time of their breaks?

(6)

What is the ratio of the length of a side of a square to its perimeter?

(7)

The ratio of the weight of Aditya to that of his friend Archana is 8:11. Archana goes on a diet and loses 4 kg and now the ratio of their weights is 8:9. How much does Archana weigh now?

(8)

The ratio of the speeds of two cars is 6:5. If the first car covers a distance of 300 km in 5 hours, then how much distance will the second car cover in 6 hours?

(9)

A tortoise has traveled at the same speed for 19 days and has covered a distance of 285 meters. If it travels 14 more days, what is the total distance it would additionally cover?

(10) Joel's toy car can travel 126 meters in a minute, while Gita's toy car can travel 17.28 kilometers in an hour. What is the ratio of the speeds of the cars belonging to Joel and Gita? (11) Ram 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 Ram had to those Surjeet had was 42:61. Surjeet then collected 180 stamps in one day and the ratio then became 42:67. How many stamps does Ram now have? (12) Bala and Ajoy start walking to school at the same time every morning. The ratio of the distance of Bala's house to the school and Ajoy's house to the school is 10:21. If they both reach school at the same time, what is the ratio of the walking speed of Bala and Ajoy? (13) Sachin buys a car after taking a loan from a bank. The loan has to be repaid in equal installments over 4 years. If Sachin has paid Rs. 6300 in 3 months, how much more money he needs to pay back to the bank? (14) A ratio consists of two terms. If, the first one is called its antecedent, what is the second term called? (15) If the width of a rectangle is 85 cm and the perimeter of the rectangle is 4.4 m, then what is the ratio of the width of the rectangle to its length?

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Answers (1)

11:13 Step 1 According to the question, total number of students in the school = 2160 Number of girls in the school = 1170 Therefore, the number of boys in the school = Total number of students in the school - Number of girls in the school = 2160 - 1170 = 990 Step 2 The fraction of boys to the girls in the school =

990 1170

=

11 13

Step 3 Therefore, the ratio of boys to girls in the school is 11:13.

(2)

2:7 Step 1 According to the question, Iqbal's grandparents live 108 km away from his house and so, he has to travel 108 km. Total distance = 108 km Distance traveled by the bus = 24 km Therefore, the distance traveled by the train = 108 - 24 = 84 km Step 2 Fraction of the distance Iqbal travels by the bus to the distance he travels by the train =

24 84

=

2 7

Step 3 Therefore, the ratio of the distance Iqbal travels by the bus to the distance he travels by the train is 2:7




(3)

7:9 Step 1 Score made by the first team = 95 runs Number of runs required to win the match = 95 + 1 Runs already scored by the second team = 42 runs Therefore, the remaining runs to be scored to win the match = Winning score - Runs already scored = (95 + 1) - 42 = 54 Step 2 Fraction of the runs they have made to the runs they need to win the match =

42 54

=

7 9

Step 3 Thus, the ratio of the runs they have made to the runs they need to win the match is 7:9.

(4)

16, 224 Step 1 16:32::112:224 can be written as

16 32

=

112 224

Step 2 The four parts of a proportion are separated into two groups, the means and the extremes, based on their arrangement in the proportion. Reading from left-to-right, the extremes are the very first number, and the very last number. This can be remembered because they are at the extreme beginning and the extreme end. Step 3 Therefore the extremes of the proportion are 16, 224.




(5)

34:3 Step 1 According to the question, in a warehouse, the workers start their work daily at 07:15 AM and end at 04:30 PM. Total working time including breaks = 04:30 PM - 07:15 AM = 9 hours 15 minutes = 555 minutes Step 2 Time for lunch break = 25 minutes Time for coffee break = 10 minutes Since, there are two coffee breaks, the total time for coffee breaks = 2 × 10 = 20 minutes Total break time = Time for lunch break + Time for coffee breaks = 25 + 20 = 45 minutes Step 3 Total working time without breaks = 555 - 45 = 510 minutes Step 4 Now, the ratio of the time they spend on working to the time they spend on breaks, =

=

Time spent on work Time spent on breaks 510 45

= 34:3 Step 5 Therefore, the ratio of the time spent on working to the time spent on breaks is 34:3.

(6)

1:4 Step 1 We know that the length of each side of a square is equal. Step 2 Let each side of the square = x Therefore, the perimeter of a square = 4x Step 3 Fraction of the length of a side of a square to its perimeter =

x 4x

=

1 4

Step 4 Therefore, the ratio of the length of a side of a square to its perimeter is 1:4.




(7)

18 Step 1 It is given that the ratio of the weight of Aditya to that of Archana = 8:11 =

8 11

Therefore, we can assume the weights of Aditya and Archana be 8x and 11x, respectively. Step 2 Archana goes on a diet and loses 4 kg, therefore her new weight will be (11x - 4) kg. Now, the new ratio of the weight of Aditya to that of Archana =

8x 11x - 4

Step 3 By cross multiplying both sides in the above equation, we get, 8 × (11x - 4) = 72x ⇒ 88x - 32 = 72x ⇒ 88x - 72x = 32 ⇒ 16x = 32 ⇒x=

32 16

⇒x=2 Step 4 Thus, the weight of Archana = 11x - 4 = (11 × 2) - 4 = 22 - 4 = 18 kg




(8)

300 km Step 1 According to the question, the ratio of the speeds of the two cars = 6:5 =

6 5

-----(1)

Step 2 Since, the first car covers a distance of 300 km in 5 hours, the speed of the first car =

Distance Time

=

300 5

km per hour

Step 3 Let us assume that the second car covers a distance of x km in 6 hours. Speed of the second car =

Distance Time

=

x 6

km per hour

Step 4 300 Now, the ratio of the speeds of the two cars =

5 x 6

=

=

300 5

×

1800

6 x

-----(2)

5x

Step 5 By comparing the equations (1) and (2): 1800 5x

=

6 5

By cross multiplying the both sides: 1800 × 5 = (6 × 5)x ⇒

1800 × 5 6×5

=x

⇒ 300 = x ⇒ x = 300 Step 6 Therefore, we can say that the distance covered by the second car in 6 hours will be 300 km.




(9)

210 meters Step 1 It is given that a tortoise has covered a distance of 285 meters in 19 days. We know, Speed =

Distance Time

Therefore, the speed =

Distance traveled Number of days

=

285 19

= 15 meters per day Step 2 We know, Distance = Speed × Time Therefore, the total distance traveled by it in 14 days = Speed × Time = 15 × 14 = 210 meters

(10) 7:16 Step 1 As, Joel's toy car can travel 126 meters in a minute, therefore the speed of the Joel's toy car = 126 meters per minute Step 2 Gita's toy car travels in an hour = 17.28 kilometers We know that 1 kilometer = 1000 meters Therefore, 17.28 kilometers = 17.28 × 1000 meters = 17280 meters Also, 1 hour = 60 minutes Therefore, Gita's toy car travels in 60 minutes = 17280 meters Or, Gita's toy car travels in 1 minute =

17280 60

meters = 288 meters

Therefore, the speed of the Gita's toy car is 288 meters per minute Step 3 Fraction of the speed of the cars belonging to Joel and Gita =

126 288

=

7 16

Step 4 Therefore, the ratio of the speeds of the cars belonging to Joel and Gita is 7:16.




(11) 1260 Step 1 The ratio of the stamps collected by Ram and Surjeet at the end of the month is 42:61. Let the number of total stamps collected by Ram and Surjeet by the end of the month be 42x and 61x, respectively. Step 2 Now, the additional stamps collected by Surjeet in one day = 180 This means, the new number of Surjeet's stamps = 61x + 180 Step 3 On equating new ratios: 42x 61x + 180 ⇒

⇒

=

42x 61x + 180 x 61x + 180

42 67 =

=

42 67 1 67

⇒ 67x = 61x + 180 ⇒ 67x - 61x = 180 ⇒ (67 - 61)x = 180 ⇒ 6x = 180 ⇒x=

180 6

⇒ x = 30 Step 4 Stamps collected by Ram = 42x = 42 × 30 = 1260 Step 5 Therefore, the total number of stamps collected by Ram is 1260.




(12) 10:21 Step 1 We are given that Bala and Ajoy start walking to school at the same time and reach school at the same time. We can say that they both take equal time to reach the school. Step 2 Let us assume that they both take t time to reach the school. Let us also assume that d1 and d2 is the distance from Bala's house to the school and Ajoy's house to the school, respectively. Step 3 Since, we know that Speed =

Bala's speed =

Ajoy's speed =

d1 t

Distance Time

,

,

d2 t

Step 4 d1 Now, the ratio of the walking speed of Bala and Ajoy =

t d2 t

=

=

d1 t

×

t d2

d1 d2

Step 5 According to the question, the ratio of the distance of Bala's house to the school and Ajoy's house to the school =

d1 d2

=

10 21

Step 6 Therefore, we can say that the ratio of the walking speed of Bala and Ajoy =


10 21

= 10:21.



(13) Rs. 94500 Step 1 As the loan has to be repaid in equal installments over 4 years and we know that 1 year = 12 months Or, 4 years = 12 × 4 = 48 months Therefore, we can say that the loan has to be repaid in the equal installments over 48 months. Step 2 Amount paid by Sachin in 3 months = Rs. 6300 Or, the amount paid by Sachin in 1 month or monthly installment =

6300 3

= Rs. 2100

Therefore, the amount paid by Sachin in 48 months = 2100 × 48 = Rs. 100800 Step 3 The remaining amount to be paid by Sachin to the bank = Amount to be paid by Sachin in 48 months − Amount paid by Sachin in 3 months = Rs. 100800 − Rs. 6300 = Rs. 94500

(14) consequent Step 1 We know that in a ratio a : b, a is the antecedent and b is the consequent. Step 2 Therefore, the second term of a ratio is called its consequent.




(15) 17:27 Step 1 Width of the rectangle = 85 cm Perimeter of the rectangle = 4.4 m Since, 1 m = 100 cm Therefore, the perimeter of the rectangle in cm = 4.4 × 100 = 440 cm Step 2 We know that the perimeter of the rectangle = 2(length + width) Therefore, the length of the rectangle =

=

440 2

perimeter of the rectangle 2

- width

- 85

= 220 - 85 = 135 cm Step 3 Fraction of the width of the rectangle to its length =

85 135

=

17 27

Step 4 Therefore, the ratio of the width of the rectangle to its length is 17:27.



Grade 6 Ratio and Proportion In

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