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 1 of 6 pages

Question 1. 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}

In A College There Are 10 Periods Per Day Each Of 40 Minutes...

\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 2. Shane has to fill a water tank in 3 hours 40 minutes and he used 7 pipes for that. How many pipes should he use to fill the tank in 1 hour 21 minutes?

21 pipes
19 pipes
7 pipes
30 pipes

Discuss Question

Answer: Option B. -> 19 pipes
:
B
Let the number of pipes be y.

\begin{matrix} Number of pipes & 7 & y Time (in minutes) & 220 & 81 \end{matrix}

Shane Has To Fill A Water Tank in 3 Hours 40 Minutes And He...

The number of pipesand the timeare inversely proportional.
AB = constant

A_{1} \times B_{1}

A_{2} \times B_{2}

\frac{7}{y}

\frac{81}{220}

\Rightarrow y = \frac{7 \times 220}{81} = 19.01 \approx 19

Shane has to use 19 pipes to fill the tank in 1 hour 21 minutes.

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
12
13

Discuss Question

Answer: Option B. -> False
:
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 \times d

= constant

n_{1} \times d_{1}

n_{2} \times d_{2}

Using inverse proportion condition,

A Factory Requires 42 Machines To Produce A Given Number Of ...

\frac{42}{n}

\frac{54}{63}

n = \frac{42 \times 63}{54}

n = 49
So, 49 machines are required.
Hence, the statement is false.

Question 4. Given that x and y are in inverse proportion, and

y_{1}

y_{2}

are values of y corresponding to the values x1, x2 of x respectively. Which of the following is correct?

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

Discuss Question

Answer: Option B. -> x1y1=x2y2
:
B
If x and y are in inverse proportion, and

y_{1}

y_{2}

are values of y corresponding to the values

x_{1}

x_{2}

of x respectively, then

x_{1}

y_{1}

x_{2}

y_{2}

Question 5.

In the equation x (y + 4) = 1, y is

Directly proportional to x
Not proportional to x
Inversely proportional to x
Can't say

Discuss Question

Answer: Option B. -> Not proportional to x
:
B
Expanding the given equation, we get

x y + 4 x = 1

Here, x y = 1 - 4 x, whichis not a constant

. Similarly,

\frac{x}{y} = (\frac{1}{4 y} - \frac{x}{4}), whichis not a constant

So, y is notproportional to x .

Question 6. Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant.

True
False
Inversely proportional to x
Can't say

Discuss Question

Answer: Option A. -> True
:
A
Given, two quantities x and y are said to vary in inverse proportion.
Then,

x \propto \frac{1}{y}

y \propto \frac{1}{x}

.
In any case, we get

x y = constant

Hence the given statemnet is true.

Question 7. A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find the cost of painting a pole that casts a shadow 5 m long. Painting is done at the rate of ₹ 5 per cm.

₹4375
₹ 5425
₹3450
₹ 3680

Discuss Question

Answer: Option A. -> ₹4375
:
A
The ratio of the length of the pole to the length of the shadow remains constant.
The length of pole and the length of the shadow are directly proportional

\frac{A}{B}

= Constant

\frac{A_{1}}{B_{1}}

\frac{A_{2}}{B_{2}}

\frac{L e n g t h o f p o l e}{l e n g t h o f s h a d o w} = \frac{560}{320} = \frac{n}{500} (where n is length the second pole)

n = 875 cm

∴

the height of the pole = 875 cm
Cost of painting the pole = 875 x 5 = ₹ 4375

Question 8. 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, 15 boxes are required.

True
False
4,200
4,500

Discuss Question

Answer: Option A. -> True
:
A
The number of bottles and the number of boxes are in inverse proportion.
AB = constant

A_{1} \times B_{1}

A_{2} \times B_{2}

Suppose the required number of boxes is

x

A Batch Of Bottles Were Packed In 25 Boxes With 12 Bottles I...

Then,

\frac{25}{x}

\frac{20}{12}

Number of boxes, x =

\frac{(25 \times 12)}{20} = 15

Question 9. In the equation y = x + 3, y is directly proportional to x.

True
False
7
9

Discuss Question

Answer: Option B. -> False
:
B
Condition for direct proportionality is

\frac{x}{y}

= constant and condition for inverse proportionality is xy= constant
So, the given equation y = x + 3; y is neither directly nor inversely proportional to x.

Question 10. If a box of sweets 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?

Discuss Question

Answer: Option B. -> 6
:
B
As the number of children increases, the number of sweets for each decreases. It is an inverse proportion.
Let the required number of sweets be x.