Direct And Inverse Proportions(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

DIRECT AND INVERSE PROPORTIONS MCQs

Total Questions : 58 | Page 3 of 6 pages

Question 21. 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)

Discuss Question

Answer: Option C. -> 420
:
C
Let h represents the height of the tower that casts 300 m long shadow.

An Electric Pole, 14 Metres High, Casts A Shadow Of 10 Metre...

\frac{14}{h} = \frac{10}{300}

10 x h = 14 x 300
h = 420 metres

Question 22. 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?

Discuss Question

Answer: Option B. -> 13
:
B
Let the required number of days with 30 men working for 6 hours be x.

\begin{matrix} Number of men & 39 & 30 Number of hours & 5 & 6 Number of days & 12 & x \end{matrix}

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

\Rightarrow 39 \times 12 \times 5 = 30 \times x \times 6 x = \frac{39 \times 12 \times 5}{30 \times 6} x = 13 days

Question 23. Given that x and y are in direct proportion, and

y_{1}, y_{2}

are values of

y

corresponding to the values

x_{1}, x_{2}

x

respectively. Which of the following is correct?

x1y2=x2y1
x1y1=x2y2
x1x2=y1y2
x1y1 = y2x2

Discuss Question

Answer: Option A. -> x1y2=x2y1
:
A
When

x

and

y

are in direct proportion, we can write

\frac{x_{1}}{y_{1}} = \frac{x_{2}}{y_{2}}

[

y_{1}, y_{2}

are values of

y

corresponding to the values

x_{1}, x_{2}

x

respectively] which gives

x_{1} y_{2} = x_{2} y_{1}

Question 24. A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Discuss Question

Answer: Option D. -> 700
:
D
Given, the number of bottles that can be filled by the machine in 6 hours is840.
Hence, the number of bottles it can fill in 1 hour

= \frac{840}{6}

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

= 140 \times 5

= 700 bottles

Question 25. 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

Discuss Question

Answer: Option C. -> 3840
:
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 =

\frac{480}{6}

= 80 bottles
Hence the number of bottles that can be filled in 2 days = 80

\times

\times

24(

∵

Number of hours in a day = 24)
=3840 bottles

Question 26. 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

Discuss Question

Answer: Option B. -> 11
:
B
Given distance s is directly proportional to square of time t.
That is:

s = k . t^{2} 20 = 4 k k = 5 So, s = 5 t^{2} 605 = 5 t^{2}

t = 11 seconds

Question 27. 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

Discuss Question

Answer: Option A. -> A
:
A
As Raghu goes at same speed ,

\frac{D i s t a n c e}{T i m e}

remains constant.
Assume that the distance covered in 4 hours be x.

Cities A,B And C Are At A Distance Of 45 Km, 50 Km And 55 Km...

10x = 4 x 60 x 2

x = 48 k m

.
Hence Raghu can reach city A in given time.

Question 28. 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
___

Discuss Question

:
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 lastfor 4 days.

Question 29.

In a college there are 10 periods per day each of 40 minutes. The students were protesting to reduce the number of periods but the Principal did not want to reduce the working hours. What should be the working hours of each period if Principal reduces the number of periods to 8?

30 minutes
55 minutes
50 minutes
45 minutes

Discuss Question

Answer: Option C. -> 50 minutes
:
C

When number of periods is 10, time for each period is 40 mins.
Let the time for each period be x mins when number of periods is changed to 8.
AB = constant
$A_{1} \times B_{1}$ = $A_{2} \times B_{2}$

$\Rightarrow x = \frac{10 \times 40}{8} = 50 m i n u t e s$ .

The principal should make each period of 50 mins.

Question 30.

Sophia was counting the number of crystals in 5kg of sugar. Can you help her to find the number of crystals in 5kg without actual counting, if 12kg of sugar contains 24 x $10^{4}$ crystals?

2 x $10^{4}$
1 × $10^{5}$
2.4 x $10^{6}$
24 x $10^{2}$

Discuss Question

Answer: Option B. -> 1 ×

10^{5}

:
B

$\begin{matrix} W e i g h t o f s u g a r & 12 & 5 N u m b e r o f c r y s t a l s & 24 \times 10^{4} & y \end{matrix}$
This situation follows direct proportionality.