Maths Inequality Questions Quiz for Syndicate Bank, Canara Bank PO and IBPS Clerk Mains Exams
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Directions: Each question below contains a statement followed by Quantity I and Quantity II. You have to study the information along with the question and compare the value derived from Quantity I and Quantity II, then anwer:

1.
Quantity I: Speed of boat in still water, if a man can travel 54 km downstream in 9 hours and 40 km upstream in 10 hours.
Quantity II: Speed of boat in still water, if a man can travel 45 km downstream in 9 hours and the speed of stream is 1 kmph.

A.
Quantity I ≤ Quantity II
B.
Quantity I ≥ Quantity II
C.
Quantity I > Quantity II
D.
Quantity I < Quantity II
E.
Quantity I = Quantity II

Answer: Option
C

Explanation:

Quantity I:
Let speed of boat = x kmph, speed of stream = y kmph

upstream speed = x – y, downstram speed = x + y

x + y = 6 ....1

x – y = 4 ....2

equation 1 + equation 2

x = 5

speed of boat = 5 kmph

Quantity II:
Let speed of boat = x kmph, speed of stream = 1 kmph

downstream speed = x + 1

5 – 1 = x

x = 4

Speed of boat = 4 kmph

Quantity I > Quantity II

Hence, option C is correct.

2.
Quantity I: Age of mother, if the age of Smiti is 1/7th of her mother's age and after 5 years Smiti's age will be 12 years.
Quantity II: Age of mother, if the ratio of the ages of Sukriti and her mother is 3 : 7 and after 3 years the ratio of their ages will be 6 : 13.

A.
Quantity I ≤ Quantity II
B.
Quantity I ≥ Quantity II
C.
Quantity I > Quantity II
D.
Quantity I < Quantity II
E.
Quantity I = Quantity II

Answer: Option
E

Explanation:

Quantity I:
Smiti's age after 5 years = 12 years

Present age of Smiti = 7 years

Mother's age
= Smiti's age
7

Mother's age = 7 × 7 = 49 years

Quantity II: Let Sukriti's age = 3x, Mother's age = 7x

According to the statement,

3x + 3 : 7x + 3 = 6 : 13

13 (3x + 3) = 6 (7x + 3)

39x + 39 = 42x + 18

39 – 18 = 42x – 39x

21 = 3x

x = 7

Mother's age = 7 × 7 = 49 years

Quantity I = Quantity II

Hence, option E is correct.

3.
Quantity I: A bag contains 3 green, 2 yellow and 3 purple balls. Two balls are drawn at random, what is the probability that no ball is purple.

Quantity II: (7x – 8) (14x – 5) = 0
A.
Quantity I ≤ Quantity II
B.
Quantity I > Quantity II
C.
Quantity I = Quantity II
D.
Quantity I < Quantity II
E.
Quantity I ≥ Quantity II

Answer: Option
A

Explanation:

Quantity I:
Favourable oucomes = ^{5} C_{2 } = 10
Total outcomes = ^{8} C_{2} = 28
Probability = 10/ 28 = 5/ 14
Quantity II:
(7x – 8) (14x – 5) = 0
7x – 8 = 0, 14x – 5 = 0
x = 8/7, 5/ 14
Quantity I ≤ Quantity II
Hence, option A is correct.

4.
What is the area of the rectangle?
Quantity I: The area of the rectangle is equal to the area of the square whose side is 24 cm.
Quantity II: The perimeter of the rectangle is 88cm, if the ratio of the length and the breadth of the rectangle is 6 : 5.

A.
Quantity I = Quantity II
B.
Quantity I < Quantity II
C.
Quantity I ≤ Quantity II
D.
Quantity I ≥ Quantity II
E.
Quantity I > Quantity II

Answer: Option
E

Explanation:

Quantity I:
Area of the square = 24 × 24
= 576 cm^{2}
Area of the square = Area of the rectangle
Area of the rectangle = 576 cm^{2}
Quantity II:
Length of the rectangle = 6x, Breadth = 5x
Perimeter = 88
2 (l + b) = 88
6x + 5x = 44
11x = 44
x = 4
Length = 24cm, breadth = 20cm
Area of the rectangle = 24 × 20
= 480 cm^{2}
Quantity I > Quantity II
Hence, option E is correct.

5.
Anuj can do the half of the work in 12 days and Manoj can do the whole work in 30 days.
Quantity I: In how many days will Anuj and Manoj do the whole work?
Quantity II: If Anuj starts the work and works for 4 days, after that Manoj join him, in how many days will the whole work be completed?

A.
Quantity I ≤ Quantity II
B.
Quantity I ≥ Quantity II
C.
Quantity I > Quantity II
D.
Quantity I < Quantity II
E.
Quantity I = Quantity II

Answer: Option
D

Explanation:

Anuj can do the half in 12 days so he can do the whole work in 24 days. Manoj can do the whole work in 30 days.

Quantity I:
Anuj and Monoj can do the whole work together =
1

Quantity II:
Anuj's 4 day work =
4
=
1
24
6

Remaining work = 1 –
1
=
5
6
6

Anuj and Manoj can do the remaining work,

Total time =
100
+ 4 =
136
9
9

Quantity I < Quantity II

Hence, option D is correct.