# Free Direct and Inverse Proportions 01 Practice Test - 8th Grade

### Question 1

39 men can build a bridge in 12 days, working 5 hours a day. In how many days will 30 men, working 6 hours a day, complete the work?

10

13

14

15

#### SOLUTION

Solution :B

Let the required number of days with 30 men working for 6 hours be x.

Number of men3930Number of hours56Number of days12x

Number of men, number of hours and number of days are inversely proportional and work done is constant in both the cases, hence

⇒39×12×5=30× x ×6x=39×12×530×6x=13 days

### Question 2

A ball falls vertically after being dropped. The ball falls a distance d metres in a time of t seconds. d is directly proportional to the square of t.

The ball falls 20 metres in a time of 2 seconds.

The time (in seconds) that the ball takes to fall 605 m is

10

11

12

13

#### SOLUTION

Solution :B

Given distance s is directly proportional to square of time t.

That is:

s=k.t220=4kk=5So,s=5t2605=5t2t = 11 seconds

### Question 3

A factory requires 42 machines to produce a given number of articles in 63 days.

The number of machines required to produce the same number of articles in 54 days is 48.

True

False

#### SOLUTION

Solution :B

Let the required number of machines be denoted by 'n' and number of days taken be 'd'.

As number of machines increases, the number of days required to make articles decreases, hence they are inversely proportional.

n×d = constant

n1×d1 = n2×d2Using inverse proportion condition,

42n = 5463

n=42×6354

n = 49

So, 49 machines are required.

Hence, the statement is false.

### Question 4

A farmer has enough food to feed 20 cattle for 6 days. The number of days food will last if there were 10 more cattle is

#### SOLUTION

Solution :As animals increases, the number of days decreases. This is in inverse proportion.

Let the required number of days be t

20 x 6 = 30 x t

t = 4

So, the food will last for 4 days.

### Question 5

A machine in a soft drink factory fills 480 bottles in six hours. How many bottles will it fill in 2 days?

4800

960

3840

2840

#### SOLUTION

Solution :C

Given, the number of bottles can be filled by the machine in 6 hours = 480

Hence number of bottles it can fill in 1 hour = 4806= 80 bottles

Hence the number of bottles that can be filled in 2 days = 80 × 2 × 24 (∵ Number of hours in a day = 24)

= 3840 bottles

### Question 6

A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

400

500

600

700

#### SOLUTION

Solution :D

Given, the number of bottles that can be filled by the machine in 6 hours is 840.

Hence, the number of bottles it can fill in 1 hour

=8406

= 140 bottlesHence number of bottles that can be filled in 5 hours

=140× 5

= 700 bottles

### Question 7

An electric pole, 14 metres high, casts a shadow of 10 metres. The height of a tower that casts a shadow of 300 metres under similar conditions is: (in metres)

140

480

420

280

#### SOLUTION

Solution :C

Let h represents the height of the tower that casts 300 m long shadow.

14h=10300

10 x h = 14 x 300h = 420 metres

### Question 8

Cities A,B and C are at a distance of 45 km, 50 km and 55 km respectively from Raghu's home. He observed that he can cover 2 km in 10 minutes on his cycle. If he has 4 hours time limit, which city he can reach on cycle if he travels at observed speed?

A

B

C

He cannot reach any city

#### SOLUTION

Solution :A

As Raghu goes at same speed , DistanceTime remains constant.

Assume that the distance covered in 4 hours be x.

10x = 4 x 60 x 2

x=48 km.

Hence Raghu can reach city A in given time.

### Question 9

Consider six squares with sides of different lengths.The length of side of square is in direct proportion to:

Perimeter of the square

Area of the square

Diagonal of square

Perimeter of squareArea of square

#### SOLUTION

Solution :A and C

Length of squarePerimeter of square=a4a=14

which is a constant.Length of squareArea of square=aa2=1a

which is not constant.

Length of squareLength of diagonal=1√2

which is constant.Hence, length of a square is in direct proportion with its perimeter and diagonal.

### Question 10

Given that x and y are in direct proportion, and y1,y2 are values of y corresponding to the values x1,x2 of x respectively. Which of the following is correct?

#### SOLUTION

Solution :A

When x and y are in direct proportion, we can write x1y1=x2y2

[y1,y2 are values of y corresponding to the values x1,x2 of x respectively] which gives x1y2=x2y1.