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Question 1

Following are the car parking charges near a railway station upto

4 hrs Rs60

8hrs Rs100

12hrs Rs140

24hrs Rs180

Check if the parking charges are in direct proportion to the parking time.


Solution:
Number of hours Parking Charges
4 60
8 100
12 140
24 180

If number of hours increases, the parking charges also increases. So it is a direct proportion.
 

Question 2

A mixture of paint is prepared by mixing 1 part of red pigments with 8 paints of base.

(a) In the following table, find the parts of base that need to be added

Parts of red pigment

1

4

7

12

20

Parts of base

8

       

(b) If 1 part of a red pigment requires 75ml of base, how much red pigment should we mix with 1800ml of base?


Solution:
More parts of red pigments, then more would be the parts of base. This is a direct proportion.

i.

ii.

iii.

iv.

Parts of red pigment

1

4

7

12

20

Parts of base

8

32

56

96

160

(b)

Part of red pigment

1

x

Part of base (ml)

75

1800



Question 3

A machine in a soft drink factory fills 840 bottles in 6hrs. How many bottles will it fill in 5 hrs?


Solution:

Number of bottles

840

x

Time

6

5



Question 4

A photograph of a bacteria enlarged 50,000 times attains a length of 5cm. What is the actual length of the bacteria? If the photograph is enlarged 20000 times only. What would be its enlarged length.


Solution:
Actual length

Enlarged length = 2cm.

Question 6

Suppose 2 kg of sugar contains crystals. How many sugar crystals are there in (i) 5 kg of sugar (ii) 1.2 kg of sugar?


Solution:

Weight of sugar

2

5

1.2

Crustals

9x106

x

y

crystals

crystals

Question 7

Rashmi has a road map with a scale of 1 cm representing 18 km, she drives on a road for 72 km. What would be her distance covered in the map?


Solution:

1 cm : 18 km

? = 72 km

Or

Distance covered in the map = 4 cm.

Question 8

A 5m 60cm high vertical pole casts a shadow 3m 20cm long. Find at the same time (i) the length of the shadow cast by another pole 10m 50cm high (ii) the height of a pole which casts a shadow of 5m long.


Solution:

Height

5.6m

10.5m

y

Length

3.2m

x

5

(i)

(ii) .

Question 9

A loaded truck travles 14km in 25 minutes. If the speed remains the same, how far can it travel in 5 hrs?


Solution:

Distance (km)

14

x

Time (min)

25

300

The truck can travel 168km in 5 hrs.

Question 10

1. Which of the following are in inverse proportion?

i. The number of workers on a job and time to complete the job.

ii. The time taken for a journey and the distance travelled in a uniform speed.

iii. Area of cultivated land & the crop harvested.

iv. The time taken for a fixed journey and the speed of the vehicle.

v. The population of a country and the area of land per person.


Solution:
i. The number of workers increases, the time taken to complete the job decreases. So it is a inverse proportion.

ii. Since the speed is uniform, the distance covered would be directly proportional to time.

It is not an inverse proportion.

iii. Since the area of cultivated land is directly proportional to the crop harvested, it is not an inverse variation.

iv. As the speed of the vehicle increases, the time taken for a journey decreases. It is a inverse proportion.

v. If the population of a country increases, the area of land per person decrease. So it is a inverse proportion.

Question 11

In a television game show the prize money of Rs1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

 


Solution:

Number of winners

1

2

4

5

8

10

20

Prize for each winner (in Rs)

1,00,000

50,000


Since the number of winners increases, the prize of the amount decreases, so it is inverse proportion.


 

Question 12

Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

 

Number of spokes

4

6

8

10

12

Angle between a pair of consecutive spokes

90°

60°

x1

x2

x3


(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes?

(iii) How many spokes would be needed, if the angle between a pair of consecutive spoke is 40°?


Solution:

(i) Yes, it is inverse proportion

(ii)

(iii)

9 = y

9 spokes are needed .

Question 13

If a boxes of sweet is divided among 24 children, they will get 5 sweets each. How many would each get if the number of children is reduced by 4?


Solution:

Each child will get 6 sweets.

Question 14

A farmer has enough food to fed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?


Solution:

The food will last up to 4 days.

Question 15

A contractor estimates that 3 persons could rewire jasminder's house in 4 days. If he uses 4 persons instead of three, how long should they take to complete the job?


Solution:

Number of days

4

x

Number of workers

3

4

3 days are required to complete the job.

Question 16

A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box how many boxes would be filled?


Solution:

Number of boxes

25

x

Number of bottles in each box

12

20

Number of boxes = 15.

Question 17

A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?


Solution:

Number of machines

42

x

Number of articles produced (days)

63

54

49 machines are required.

Question 18

A car takes 2 hours to reach a destination by travelling at the speed of 60km/h. How long will it take when the car travels at the speed of 80km/hr?


Solution:

Speed (km/h)

60

80

Time(hrs)

2

x

.

Question 19

Two persons could fit new windows in a house in 3 days

i. One of the persons fell ill before the work started, how long could the job take now?

ii. How many persons would be needed to fit the window is one day?


Solution:

Number of persons

2

1

y

Number of days

3

x

1

(i)

Number of days is 6.

(ii)

Number of persons required = 6.

Question 20

A school has 8 periods a day each of 45 minutes duration. How long each period be, if the school has 9 periods a day assuming the number of school hours to be the same?

 


Solution:

Number of periods

8

9

Duration (min)

45

x


Duration of each period = 40 minutes.





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