Direct And Inverse Proportions Test

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Direct And Inverse Proportions Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

If x : y = 3 : 4 and 4 : x = 2 : 3, then the value of y is

A
8

B
10

C
12

D
14

Solution

and

So, ... (1)

Putting the value of x in (1), we get
24 = 3y
y = 8
Question 2
1 / -0

If x varies inversely as y, and x = 15 when y = 9, then what is the value of y when x = 25?

A
5

B

C
10

D

Solution

As x and y vary inversely, we can say that their product is constant.
So, xy = Constant
Question 3
1 / -0

If x varies directly as y², and x = 6 when y = 8, then what is the value of x when y is 24?

A
21

B
35

C
54

D
62

Solution

x and y² are directly proportional to each other.
This means
Question 4
1 / -0

If , then the value of x is

A
27

B
49

C
63

D
81

Solution

x = 49
Question 5
1 / -0

x and y vary in inverse proportion. When x is 16, y is 4. Which of the following is a possible pair of corresponding values of x and y?

A
2 and 32

B
34 and 4

C
14 and 4

D
15 and 2

Solution

For inverse proportion, xy = constant or x₁y₁= x₂y₂
x₁y₁= 16 × 4 = 64 (given)
Out of all the four given options, only 2 and 32 satisfy the condition of inverse proportionality because .
Hence, option (1) is correct.
Question 6
1 / -0

Which of the following statements is/are INCORRECT?

A
The length of a side of a rectangle and its perimeter vary directly with each other.

B
If time remains constant, then speed is directly proportional to distance.

C
The area of a triangle and the height vary indirectly with each other.

D
All of these

Solution

(1) The length of a side of a rectangle and its perimeter vary directly with each other.
The above statement is true.
As we know,
Perimeter of a rectangle =

(2) If time remains constant, then speed is directly proportional to distance.
This statement is also correct.

(3) The area of a triangle and the height vary indirectly with each other.
This statement is incorrect as:

Area of a triangle =

Thus, the height and the area of a triangle vary directly with each other.
Question 7
1 / -0

If A : B = 4 : 5 and B : C = 6 : 7, then C : A is equal to

A
11 : 16

B
12 : 17

C
31 : 21

D
35 : 24

Solution

... (1)

... (2)

Equating the values of B from (1) and (2),

Or and

Question 8

1 / -0

Match the following:

	Column I	Column II
P	x and y are in direct proportion, and x = 40 when y = 150. If x = 60, then y=	(i) 140
Q	x varies inversely as y, and x = 14 when y = 320. If x = 32, then y=	(ii) 225
R	x varies directly as y, and y = 80 when x = 150. If x= 120, then y =	(iii) 64
S	x varies inversely as y,and y = 600 when x = 30. If x = 120, then y=	(iv) 150

P - ii, Q - i, R - iii, S - iv

P - i, Q - ii, R - iii, S - iv

P - iv, Q - iii, R - i, S - ii

P - i, Q - iv, R - iii, S - ii

Solution

(P)

(Q)

(R)

(S)

Question 9
1 / -0

When x = 3, 18, 54, …, y = 6, 36, 108, ... Then, x and y are

A
in direct proportion

B
in inverse proportion

C
neither in direct nor in inverse proportion

D
None of these

Solution

= = Constant

Therefore, x and y are in direct proportion.
Question 10
1 / -0

If two quantities x and y vary directly with each other, then

A
remains constant

B
(x - y) remains constant

C
(x + y) remains constant

D
(y × x) remains constant

Solution

If two quantities x and y vary directly with each other, then remains constant.
Question 11
1 / -0

If 10 men can do a piece of work in 12 days, then how long will 12 men take to do the same work?

A
8 days

B
10 days

C
12 days

D
14 days

Solution

Let the required number of days be x.
As per the information given in the question, it is a case of inverse proportion.

Number of men 10 12

Number of days 12 x

10 12 = 12x
120 = 12x
x = 10
Question 12
1 / -0

A salesman receives a commission of Rs. 85.00 on the sales of Rs. 1200. The commission he will get on the sales of Rs. 600 is

A
Rs. 10.5

B
Rs. 22.5

C
Rs. 35.5

D
Rs. 42.5

Solution

Let the commission received on the sale of Rs. 600 be Rs. y.

Sales 1200 600

Commission 85 y

This is a case of direct proportion.

Hence,

So, the salesman will receive Rs. 42.5 on the sales of Rs. 600.
Question 13
1 / -0

In a class, on an average, 6 chocolates are shared in a group of 8 students. How many students are present in the class if 30 chocolates are shared?

A
10

B
20

C
30

D
40

Solution

Number of chocolates 6 30

Number of students 8 ?

Number of students
Question 14
1 / -0

In a school camp, there is sufficient food for 110 students for 24 days. If 50 students leave the camp, how long would the food last?

A
19 days

B
28 days

C
35 days

D
44 days

Solution

Let the required number of days be y.

Number of students 110 110 - 50 = 60

Number of days 24 y

It is a case of inverse proportion.
Hence,

y =
y = 44

The food would last for 44 days.
Question 15
1 / -0

A person has enough money to buy 60 curtains worth Rs. 660 each. If each curtain were to cost Rs. 60 more, then the number of curtains he would be able to buy with that amount of money would be

A
40

B
45

C
50

D
55

Solution

Cost of one curtain = Rs. 660
Cost of 60 curtains = 660 60 = Rs. 39,600
New cost of one curtain = Rs. (660 + 60) = Rs. 720
So, number of curtains that can be bought with Rs. 39,600 =
Question 16
1 / -0

A painter is paid Rs. 600 for 15 days of work. If he receives Rs. 25,000, then for how many days does he work?

A
625

B
615

C
525

D
575

Solution

Let the required number of days be x.

Amount (in Rs.) 600 25,000

Number of days 15 x

According to direct proportion,

So, x = 625
Question 17
1 / -0

Varun enlarged the picture of a lion 2000 times for his project to maintain its length of 250 cm. What was the actual length of the picture?

A
5.614 cm

B
4 cm

C
2.5 cm

D
0.125 cm

Solution

Let the actual length of the picture be x cm.

Enlargement of the picture 2000 times 1 time

Length 250 cm x

So, according to direct proportion,

x =

x = 0.125 cm
Question 18
1 / -0

Priya has enough money to buy 80 bed-sheets worth Rs. 450 each. How many bed-sheets can she buy with the same amount of money if she gets Rs. 150 off on each bed-sheet?

A
150

B
145

C
120

D
112

Solution

Let the number of bed-sheets that she can buy after reduction in the price be x.

Number of bed-sheets 80 x

Cost of each bed-sheet 450 450 - 150 = 300

Thus, according to inverse proportion,
80 × 450 = x × 300

x =
x = 120
Question 19
1 / -0

A cistern has two taps which fill it in 15 min and 18 min, respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 25 min. How long will the waste pipe take to empty a full cistern?

A
min

B
min

C
12 min

D
min

Solution

Time required to fill the cistern by first pipe = 15 min
Time required to fill the cistern by second pipe = 18 min
Due to a waste pipe, time taken to fill this cistern by both pipes together = 25 min
Now, according to the question,
Time required emptying the cistern by waste pipe = = 12min
Question 20
1 / -0

In 3 days, Neeraj uses of water to irrigate his entire field. In how many days can he utilise of water?

A
27

B
30

C
33

D
39

Solution

Let the required number of days be x.
According to direct proportion,

Question 21

1 / -0

State 'T' for true and 'F' for false and choose the correct option with the help of the table given below.

(i) If p and q are in inverse proportion, then (p + 1) and (q + 1) are in direct proportion.
(ii) If x and y are in direct proportion, then (x - 2) and (y - 2) are also in direct proportion.
(iii) Two quantities x and y are said to be vary inversely with each other if

= k, where k is a positive constant.
(iv) When distance is kept fixed, then speed varies inversely with time.

	(i)	(ii)	(iii)	(iv)
A	F	F	F	T
B	T	T	F	F
C	T	T	T	F
D	F	F	T	T

A

B

C

D

Solution

(i) If p and q are in inverse proportion, then (p + 1) and (q + 1) are in direct proportion.
This statement is false, because if p and q are in inverse proportion, then we cannot say anything certainly about (p + 1) and (q + 1) whether they are directly proportional or inversely proportional.

(ii) If x and y are in direct proportion, then (x - 2) and (y - 2) are also in direct proportion.
This statement is false because if x and y are in inverse proportion, then we cannot say anything certainly about (x - 2) and (y - 2) whether they are directly proportional or inversely proportional.

(iii) Two quantities x and y are said to be vary inversely with each other if

= k ,where k is a positive constant.
This statement is false because two quantities x and y are said to vary directly with each other if

= k, where k is a positive constant.

(iv) When distance is kept fixed, then speed varies inversely with time.
This statement is true because Distance = Speed x Time. Thus, if distance remains constant, then time and speed vary inversely.

Question 22

1 / -0

Fill in the blanks with the help of the table given below.

(i) The area and the length of a rectangle vary ___A____ with each other.
(ii) If two quantities x and y vary directly with each other, then the ___B____ of their corresponding value remains constant.
(iii) Given p and q are in direct proportion, if p is doubled, then the value of q will be ____C_____.

	A	B	C
P	directly	ratio	doubled
Q	inversely	product	halved
R	directly	product	doubled
S	inversely	ratio	halved

S

R

Q

P

Solution

(i) The area and the length of a rectangle vary ___A____ with each other.
Area of a rectangle = Length × Breadth
So, the area of a rectangle is directly proportional to its length.

(ii) If two quantities x and y vary directly with each other, then the ___B____ of their corresponding value remains constant.
The ratio of x to y is constant.
If two quantities x and y vary directly with each other, then the ratio of their corresponding value remains constant.

(iii) Given p and q are in direct proportion, if p is doubled, then the value of q will be doubled.

Question 23

1 / -0

Match the following:

Column I	Column II
(P) If the cost of 95 m of a certain kind of cloth is Rs. 1330, then what will be the cost (in Rs.) of 120 m of such cloth?	(i) 1680
(Q) 60 cows can graze a field in 6 days. How many cows will graze the same field in 10 days?	(ii) 40
(R) 20 workers can reap a field in 40 days. For reaping the same field in 20 days, how many workers are required?	(iii) 36
(S) Sahil types 1620 words in one hour. What is his GWPM (gross words per minute)?	(iv) 27

P - (i), Q - (iii), R - (ii), S - (iv)

P - (i), Q - (iii), R - (iv), S - (ii)

P - (ii), Q - (iii), R - (i), S - (iv)

P - (i), Q - (ii), R - (iii), S - (iv)

Solution

(P) If the cost of 95 m of a certain kind of cloth is Rs. 1330, then what will be the cost (in Rs.) of 120 m of such cloth?
Cost of 95 m of cloth = Rs. 1330

Cost of 1 m of cloth = Rs. = Rs. 14

Thus, cost of 120 m of cloth = 14 120 = Rs. 1680

(Q) 60 cows can graze a field in 6 days. How many cows will graze the same field in 10 days?
Let the required number of cows be x.

As it is a case of inverse variation;
60 × 6 = x × 10
x = (60 × 6)/10 = 36
Therefore, 36 cows will graze the same field in 10 days.

(R) 20 workers can reap a field in 40 days. For reaping the same field in 20 days, how many workers are required?

Let the required number of workers be x.
As it is a case of inverse variation;
20 × 40 = x × 20
x = (20 × 40)/20 = 40
Therefore, 40 workers are required to reap the same field.

(S) Sahil types 1620 words in one hour. What is his GWPM (gross words per minute)?
Sahil types 1620 words in one hour.
Let the number of words be x.
As it is a case of direct proportion;

x = 27

His GWPM (gross words per minute) is 27.

Question 24

1 / -0

A labourer is paid Rs. 140.50 for 5 days.

(i) What amount will he get for 25 days?
(ii) For how many days will he be working to get Rs. 4215?

	(i)	(ii)
A	Rs. 702.5	150
B	Rs. 525.5	150
C	Rs. 702.5	180
D	Rs. 525.5	180

A

B

C

D

Solution

Amount paid	= 140.5	= ?
Number of days	= 5	= 25

Since it is a case of direct proportion;

=
= Rs. 702.5

(ii) Let be the number of days he will work for Rs. 770.

Amount paid in rupees	= 140.5	= 4215
Number of days	5

It is a case of direct proportion.

Therefore,

= = 150

Question 25
1 / -0

Which of the following tables show(s) direct proportion?

(i)

x 5 15 2.9

y 15 45 8.7

(ii)

x 2 6 4.6

y 3 9 6.9

(iii)

x 3 5 5.4

y 4 8 7.2

A
Only (i)

B
Only (ii)

C
Both (i) and (ii)

D
Only (iii)

Solution

(i)
Thus, this tables shows direct proportion.

(ii)
Thus, this table shows direct proportion.

(iii)
Thus, this table does not show direct proportion.

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Re-Attempt Weekly Quiz Competition

Number of bed-sheets	80	x
Cost of each bed-sheet	450	450 - 150 = 300

Sales	1200	600
Commission	85	y

Enlargement of the picture	2000 times	1 time
Length	250 cm	x

x	5	15	2.9
y	15	45	8.7

x	2	6	4.6
y	3	9	6.9

Direct And Inverse Proportions Test - 6

Result

Direct And Inverse Proportions Test - 6

Score

-

Rank

-

SHARING IS CARING

Question 1

8

10

12

14

Solution

Question 2

5

10

Solution

Question 3

21

35

54

62

Solution

Question 4

27

49

63

81

Solution

Question 5

2 and 32

34 and 4

14 and 4

15 and 2

Solution

Question 6

The length of a side of a rectangle and its perimeter vary directly with each other.

If time remains constant, then speed is directly proportional to distance.

The area of a triangle and the height vary indirectly with each other.

All of these

Solution

Question 7

11 : 16

12 : 17

31 : 21

35 : 24

Solution

Question 8

P - ii, Q - i, R - iii, S - iv

P - i, Q - ii, R - iii, S - iv

P - iv, Q - iii, R - i, S - ii

P - i, Q - iv, R - iii, S - ii

Solution

Question 9

in direct proportion

in inverse proportion

neither in direct nor in inverse proportion

None of these

Solution

Question 10

remains constant

(x - y) remains constant

(x + y) remains constant

(y × x) remains constant

Solution

Question 11

8 days

10 days

12 days

14 days

Solution

Question 12

Rs. 10.5

Rs. 22.5

Rs. 35.5

Rs. 42.5

Solution

Question 13

10