Maths Inequality Questions For Bank PO | Free Maths Study Material For SBI PO 2019, IBPS PO 2019

Directions: In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered)
1
In a mixture of 80 litres acid and water, the ratio of acid to water is 3 : 5. 
 
Quantity I : when half of the mixture was withdrawn and in the same quantity a new solution X of acid and water was added then what should be concentration of acid in the new solution X if the ratio of acid to water in the mixture become 1 : 1 
 
Quantity II : 50% 
» Explain it
A
The quantity of acid =  80 × 3  = 30 litres
8

The quantity of Water =  80 × 5  = 50 litres
8

When half of the solution was withdrawn then acid and water would be withdrawn in the same ratio
The reaming quantity of acid =  30  = 15 litres
2

And the remaining quantity of water =  50  = 25 litres
2

Now, in the same quantity a new solution x of acid and water was added then the ratio become 1 : 1

It means, Acid = 40 litres and water = 40 litres

The quantity of acid in the new solution x = 40 – 15 = 25 litres

The quantity of water in the new solution = 40 – 25 = 15 litres
 
The reqd. % =  25 × 100  =  250  = 62.5%
40 4

Hence, option A is correct.

2
In a family of three members, A, B, and C the difference between A’s age and B’s age is same as the difference between B’s age and C’s age. The average of their age is 45 years and the age of eldest member of the family is 60 years. 
 
Quantity I : What is the age of smallest member of the family?   
 
Quantity II : 14 years ago, what was the average of the age of smallest member and that of eldest member of the family? 
» Explain it
C
According to the question,

A – B = B – C

2B = A + C ----- (i)

And A + B + C = 45 × 3 = 135 years ------ (ii)

Solve this equation or we can say that the age of A, B, and C are in athematic progression

Were let the common difference = D then

The age of three members X – D, X, X + D years

X – D + X + X + D = 45 × 3

3X = 45 × 3

X = 45 years

The age of eldest member = X + D = 45 + D = 60

D = 15 years

Quantity I : The age of smallest member of the family = 45 – d = 45 – 15 = 30 years

Quantity II : 14 years ago, Smallest Member’s age = 30 – 14 = 16 years

And Eldest member’s age = 60 – 14 = 46 years

The sum = 16 + 46 = 62 years

The reqd. average =  62  = 31 years
2

Therefore, Quantity : I < Quantity : II

Hence, option C is correct.
 
3
Quantity I : In a school, 50% of the total number of girls is equal to 30% of the total number of boys then the number of girls is what percentage of the total number of students of the school? 
 
Quantity II : In a school, 33.33% of the total number of girls is equal to 66.67% of the total number of boys then the total number of girls is what percentage of the total number of students of the school? 
» Explain it
C
Quantity I:

Let the number of girls = x and the number of boys = y then

50% of x = 30% of y

5x = 3y

x : y =  3
5

x = number of girls = 3a then y = number of boys = 5a
 
The reqd. % =  3a × 100  =  300  = 37.5%
8a 8

Quantity II:

Let the number of girls = x and the number of boys = y then

33.33% of x = 66.67% of y

x = 2y

x : y = 2 : 1

x = number of girls = 2a then y = number of boys = a
 
The reqd. % =  2a × 100  =66.67 %
3a

Therefore, Quantity : I < Quantity : II

Hence, option C is correct.
 
4
A train of length x meters travelling at the speed of 54 km per hour can cross a boy standing on a platform in 16 seconds but at the speed of 72 km per hour it can cross a platform of y meters long in 24 seconds. 
 
Quantity I : What is the length of the train? 
 
Quantity II : What is the length of the platform? 
» Explain it
E
54 km per hour =  54 × 5  = 15 meters per second
18

Quantity I:

The length of the train = 15 × 16 = 240 meters

Quantity II :
72 km per hour =  72 × 5  = 20 meters per second
18

Let the length of the platform = y meters then

(240 + y) = 20 × 24 = 480

y = 480 – 240 = 240 meters

Therefore, Quantity : I = Quantity : II

Hence, option E is correct.
5
10 litres of water were drawn from a cask full of water and it was filled with 30 litres milk then the concentration of milk in the mixture become 20%. 
 
Quantity I : Again, how many litres of mixture should be replaced with 10 litres milk so the concentration of water in the mixture will become 60%. 
 
Quantity II : What was the original quantity of water in the cask? 
» Explain it
C
Quantity I: Let the quantity of water in the cask = x litres then

x – 10 + 30 = x + 20 litres = quantity of mixture

The quantity of milk in x + 20 litres = 30 litres

According to the question, 20% of (x + 20) = 30

x + 20 = 150

x = 130 litres

And the quantity of mixture = x + 20 = 150 litres

The quantity of water = x – 10 = 120 litres

In 1 litre mixture, the quantity of water =  120  litres
150

In y litres mixture, the quantity of water =  12y  litres
15

Now, let y litres of mixtures was replaced with 10 litres of milk

Then, the quantity of mixture = 150 – y + 10 = 160 – y litres
 
60% of (160 – y) = 120 –   12y
15

96 – 0.6y = 120 – 0.8y

0.2y = 24

y = 120

Quantity II : 130 litres

Therefore, Quantity : I < Quantity : II

Hence, option C is correct.

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Folks, maths inequality is frequently asked topic in bank po and bank clerk exams, so every aspirant must be aware with it.Aspirants can easily score high by just practicing some important maths inequality question. At Smartkeeda you will find maths inequality questions in the form of quizzes and pdf form too.
So you can practice in both modes online and offline.In quantity based questions you will see questions are being asked are Profit and Loss, Partnership, Time and Work, Pipe and cistern and probability etc.
 
Here are some examples of quantity based maths questions for sbi po 2019
 
Q.1. A motorboat can travel x km upstream and x + 20 km downstream in 17.5 hours. If the ratio of the speed of the motorboat in still water to the speed of stream is 3: 1 and the difference between their speed is 4 km.
Quantity I : What is the value of x?
Quantity II : How much distance the motorboat will travel downstream in 5 hours 15 minutes?
 
A. Quantity : I > Quantity : II
B. Quantity : I ≥ Quantity : II
C. Quantity : I < Quantity : II 
D. Quantity : II ≥ Quantity : I
E. Quantity I = Quantity II or relation can't be established 
 
Q.2. Two persons, A and B together can do a piece of work in 15 days. B is 80% as efficient as A.
 
Quantity I : If they work on alternate day, starting with A then how many days will they take to complete 50% of the work?
Quantity II : How many days, B alone will take to complete 40% of the total work?
 
A. Quantity : I > Quantity : II
B. Quantity : I ≥ Quantity : II
C. Quantity : I < Quantity : II 
D. Quantity : II ≥ Quantity : I
E. Quantity I = Quantity II or relation can't be established
 
Q.3. On 1st Jan 2018, the average age of a family of 5 members is 45 years. On 1st July 2018, one of the members of the family died. On 1st Jan 2019, the average age of the family will become 32 years.
Quantity I : At what age, did the person die?
Quantity II : 100 years
 
A. Quantity : I > Quantity : II
B. Quantity : I ≥ Quantity : II
C. Quantity : I < Quantity : II 
D. Quantity : II ≥ Quantity : I
E. Quantity I = Quantity II or relation can't be established
 
For more questions you can take maths inequality given quizzes with explanation.
 
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