Mathematics - Direct and Inverse Proportions
Exam Duration: 45 Mins Total Questions : 25
If x : y = 2 : 3 and 2 : x = 1 : 2, then the value of y is________.
- (a)
1/3
- (b)
3/2
- (c)
6
- (d)
1/2
If x and y vary inversely as each other, and x = 10 when y = 6. Find y when x = 15.
- (a)
3
- (b)
4
- (c)
2
- (d)
6
If x varies directly as y2 and x = 4 when y = 5, then find x when y is 15.
- (a)
4
- (b)
9
- (c)
12
- (d)
36
if \(\frac { 1 }{ 5 } :\frac { 1 }{ x } =\frac { 1 }{ x } :\frac { 1 }{ 25 } \), then the value of x is ________.
- (a)
1.25
- (b)
1.5
- (c)
25
- (d)
2.25
x and y vary in inverse proportion. When x is 12, Y is 3. Which of the following is not a possible pair of corresponding values of x and y?
- (a)
4 and 9
- (b)
10 and 3.6
- (c)
72 and 0.5
- (d)
5 and 6
Which of the following statements is Correct?
- (a)
Length of a side of square and its area vary directly with each other.
- (b)
If one angle of a triangle is kept fixed then the measure of the remaining two angles vary inversely with each other.
- (c)
The area of circle and its diameter vary directly with each other.
- (d)
All of these
If A : B = 2 : 3 and B : C = 4 : 5, then C : A is equal to_______.
- (a)
15 : 8
- (b)
12 : 10
- (c)
8 : 5
- (d)
8 : 15
Match the following.
| Column - I | Column - II |
|---|---|
| P. x and yare in direct proportion and x = 40 when y = 120. If x = 60 then y = | (i) 160 |
| Q. x varies inversely as y and x = 12 when y = 300, if x = 24 then y = | (ii) 180 |
| R. x varies directly as y and y = 50 when x = 30, if x = 96 then y = | (iii) 130 |
| S. x varies inversely as y and y = 650 when x = 20 if x = 100 then y = | (iv) 150 |
- (a)
P\(\rightarrow\)(iv); Q\(\rightarrow\)(i); R\(\rightarrow\)(iii); S\(\rightarrow\)(ii)
- (b)
P\(\rightarrow\)(ii); Q\(\rightarrow\)(iv); R\(\rightarrow\)(iii); S\(\rightarrow\)(i)
- (c)
P\(\rightarrow\)(iv); Q\(\rightarrow\)(i); R\(\rightarrow\)(ii); S\(\rightarrow\)(iii)
- (d)
P\(\rightarrow\)(ii); Q\(\rightarrow\)(iv); R\(\rightarrow\)(i); S\(\rightarrow\)(iii)
When x = 2, 7,11,....... , Y = 8, 28, 44, .... , then x and yare in.........
- (a)
Direct proportion
- (b)
Inverse proportion
- (c)
Neither direct nor inverse proportion
- (d)
None of these
Two quantities x and y vary inversely with each other, then_________.
- (a)
x/y remains constant
- (b)
x - y remains constant
- (c)
x + y remains constant
- (d)
x x y remains constant
8 men can do a piece of work in 10 days. How long will 10 men take to do the same work?
- (a)
12 days
- (b)
8 days
- (c)
7 days
- (d)
6 days
An agent receives a commission of RS 73.00 on sales of RS 1000.00. The commission he will get on sales of RS 100.00 is________.
- (a)
Rs 7.30
- (b)
Rs 7.00
- (c)
Rs 6.00
- (d)
Rs 6.30
In a birthday party, on an average, 5 bottles of coke are served for a group of 6 children. How many friends were present at Mohit's party if 15 bottles of coke were used?
- (a)
18
- (b)
24
- (c)
30
- (d)
12
In a camp there is sufficient food for 105 soldiers for 21 days. If 42 soldiers leave the camp, then how long would the food last?
- (a)
30 days
- (b)
35 days
- (c)
65 days
- (d)
45 days
A shopkeeper has just enough money to buy 52 cycles worth Rs 525 each. If each cycle were to cost Rs 21 more, then number of cycles, he will be able to buy with that amount of money, is ________.
- (a)
40
- (b)
30
- (c)
50
- (d)
20
A labourer is paid Rs 806 for 13 days of work. If he receives Rs 1,798, then for how many days did he work?
- (a)
29
- (b)
35
- (c)
60
- (d)
40
A photograph of a bacteria enlarged 50,000 times, attains a length of 5 cm What is the actual length of the bacteria?
- (a)
2 x 10-4 cm
- (b)
103 cm
- (c)
10-4 cm
- (d)
104 cm
Raghu has enough money to buy 75 machines worth Rs 200 each. How many machines can he buy if he gets a discount of Rs 50 on each machine?
- (a)
180
- (b)
200
- (c)
150
- (d)
100
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes then are opened together in the empty cistern, time taken to fill the cistern completely is________.
- (a)
20 minutes
- (b)
10 minutes
- (c)
15 minutes
- (d)
5 minutes
In 15 days, the earth picks up 1.2 x 108 kg of dust from the atmosphere. In how many days it will pick up 4 8 x 108 kg of dust?
- (a)
50
- (b)
40
- (c)
60
- (d)
100
State 'T' for true and 'F' for false.
(i) If x and yare in direct proportion, then (x - 1) and (y - 1) are also in direct proportion.
(ii) If x and yare in inverse proportion then (x + 2) and (y + 2) are also in inverse proportion.
(iii) Two quantities x and yare said to vary directly with each other if where \(\frac { x }{ y } =k\) is a positive constant.
(iv) When distance is kept fixed, then speed and time vary inversely with each other.
- (a)
(i) (ii) (iii) (iv) T F F T - (b)
(i) (ii) (iii) (iv) T T F T - (c)
(i) (ii) (iii) (iv) F F T T - (d)
(i) (ii) (iii) (iv) T F T F
Fill In the blanks.
(i) The perimeter of circle and its diameter vary P with each other.
(ii) (ii) If two quantities p and q vary inversely with each other then Q of their corresponding values remain constant.
(iii) When x and yare in indirect proportion and if y doubles then x becomes R.
- (a)
P Q R Inversely Ratio Double - (b)
P Q R Directly Product Half - (c)
P Q R Inversely Ratio Half - (d)
P Q R Directly Product Double
Match the following.
| Column - I | Column - II |
| (P) If the cost of 93 m of a certain kind of plastic sheet is Rs 1395, then what would it cost (in Rs) to buy 105 m of such plastic sheet? | (1) 42 |
| (Q) 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days? | (2) 18 |
| (R) 18 men can reap a field in 35 days. For reaping the same field in 15 days; how many men are required? | (3) 88 |
| (S) Suneeta types 1080 words in one hour. What is her GWPM (gross words per minute)? | (4) 1575 |
- (a)
P Q R S 4 3 1 2 - (b)
P Q R S 2 1 4 3 - (c)
P Q R S 3 2 1 4 - (d)
P Q R S 1 3 2 4
A worker is paid Rs 139.20 for 3 days.
(i) What will he get in the month of June (In Rs)?
(ii) For how many days will he be working for Rs 696?
- (a)
(i) (ii) 1392 15 - (b)
(i) (ii) 15 1392 - (c)
(i) (ii) 1382 20 - (d)
(i) (ii) 1392 20
Which of the following tables shows the inverse proportion?
(i)
| x | 6 | 12 | 30 | 48 |
| y | 250 | 125 | 50 | 31.25 |
(ii)
| x | 115 | 130 | 145 | 160 |
| y | 615 | 600 | 585 | 570 |
(iii)
| x | 50 | 100 | 300 | 120 |
| y | 300 | 150 | 100 | 75 |
- (a)
Only (i)
- (b)
Both (i) and (ii)
- (c)
Both (ii) and (iii)
- (d)
None of these
