Question 1
Following are the car parking charges near a railway station uptoCheck 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
Â  Â  Â  Â 
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 
Solution:Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Height 
Length 
Mast height 
9 
? 
Actual ship 
12 
28 
Â
Â
Length of the ship in the model = 21m.
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.
(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 40Â°?
Solution:
(i) Yes, it is inverse proportion
(ii)
(iii)
9 = y
9 spokes are needed .
Question 19
Two persons could fit new windows in a house in 3 daysi. 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.