Aptitude Questions – Inequalities Set 2

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions in Inequalities which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

1. Mr. Ramesh has three daughters namely Rohini, Anita and Keerthi. Rohini is the eldest daughter of Mr. Ramesh while Keerthi is the youngest one. The present ages of all three of them are square numbers. The sum of their ages after 5 years is 44. 
   Quantity I: The age of Rohini and Anita after two years
   Quantity II: The age of Rohini and Keerthi after four years
   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 or relation cannot be established
   
   Answer & Explanation

   A. Quantity I > Quantity II
   Explanation:
   Square numbers – a, b, c
   (a + 5) + (b + 5)+ (c + 5) = 44
   a + b + c = 44 – 15 = 29
   Possible values of a, b, c = 4, 9, 16 [Out of 1, 4, 9, 16, 25]
   The age of Rohini and Anita after two years = 29; The age of Rohini and Keerthi after four years = 28
   
   
2. A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak and Ramesh in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 year respectively remains equal. 
   Quantity I: Share of Ramesh
   Quantity II: Share of Anil
   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 or relation cannot be established
   
   Answer & Explanation

   B. Quantity I < Quantity II
   Explanation:
   x*5*1/100 = y*5*2/100 = z*5*3/100
   x:y:z = 6:3:2
   Share of Ramesh = 2/11 * 8800 = 1600; Share of Anil = 6/11 * 8800 = 4800
   
   
3. Person A sold his car to Person B at a profit of 20% and B sold it to C at a profit of 10%. Person C sold it to a mechanic at a loss of 9.09%. Mechanic spent 10% of his purchasing price and then sold it at a profit of 8.33% to Person “A” once again
   Quantity I: Selling Price of A
   Quantity II: Selling Price of C
   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 or relation cannot be established
   
   Answer & Explanation

   E. Quantity I = Quantity II or relation cannot be established
   Explanation:
   A:
   CP = 100
   SP = 120
   B:
   CP = 120
   SP = 132
   C:
   CP = 132
   SP = 120
   Mechanic:
   CP = 120 + 12 = 132
   SP = 143
   
   
4. Smallest side of a right-angled triangle is 13 cm less than the side of a square of perimeter 72 cm. The second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm.
   Quantity I: Six more than the side of the right-angled triangle(not the smallest)
   Quantity II: The Sum of Hypotenuse of the right-angled triangle and the smallest side
   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 or relation cannot be established
   
   Answer & Explanation

   E. Quantity I = Quantity II or relation cannot be established
   Explanation:
   Side of square = 72/4 = 18 cm
   Smallest side of the right angled triangle = 18 – 13 = 5 cm
   Length of rectangle = 112/8 = 14 cm
   Second side of the right angled triangle = 14 – 2 = 12 cm
   Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
   
   
5. Quantity I: (x – 36)² = 0
   Quantity II: y² = 1296
   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 or relation cannot be established
   
   Answer & Explanation

   C. Quantity I ≥ Quantity II
   Explanation:
   x² – 72x + 1296 = 0
   x = 36, 36
   y² = 1296
   y = ±36
   
   
6. Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 8 hours to fill up the whole tank.
   Quantity I: x = Pipe “Q” Efficiency. y = net efficiency
   Quantity II: x = Pipe “P” Efficiency. y = net efficiency
   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 or relation cannot be established
   
   Answer & Explanation

   E. Quantity I = Quantity II or relation cannot be established
   Explanation:
   Pipe P Efficiency = 100/10 = 10%
   Pipe Q Efficiency = 100/20 = 5%
   Net Efficiency = 15%
   
   
7. In an office there are 40% female employees. 50% of the male employees are UG graduates. The total 52% of employees are UG graduates out of 1800 employees.
   Quantity I: Male Employees who are UG Graduates
   Quantity II: Female Employees who are UG Graduates
   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 or relation cannot be established
   
   Answer & Explanation

   A. Quantity I > Quantity II
   Explanation:
   Total employees = 1800
   female employees = 40%
   male employees = 60%
   50% of male employess = UG graduates = 30%
   Female employees who are UG graduates = 22%
   
   
8. Suresh spends 23% of an amount of money on an insurance policy, 33% on food, 19% on children’s education and 16% on recreation. He deposits the remaining amount of Rs. 504 in bank.
   Quantity I: Amount spend on food and insurance policy together
   Quantity II: Amount spend on children’s education and recreation together
   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 or relation cannot be established
   
   Answer & Explanation

   A. Quantity I > Quantity II
   Explanation:
   Total amount = x
   Savings(%)
   [100 – (23 + 33 + 19 + 16 )]% = 9 %
   9% of x = 504
   => x = 504 * 100/9 = 5600
   Amount spend on food and insurance policy together = 56% of 5600 = Rs.3136
   
   
9. Last year there were 610 boys in a school. The number decreased by 20 percent this year.  The number of girls is 175 percent of the total number of boys in the school this year.
   Quantity I: Total number of boys in the school this year.
   Quantity II: Half of total number of Girls in the school this year.
   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 or relation cannot be established
   
   Answer & Explanation

   A. Quantity I > Quantity II
   Explanation:
   No of boys in a school last year = 610
   No of boys in a school for this year
   610*80/100=122
   610-122=488
   No of girls =175/100 * 488=854 = 427
   
   
10. Two persons A and B start from the opposite ends of a 450 km straight track and run to and from between the two ends. The speed of the first person is 25 m/s and the speed of other is 35 m/s. They continue their motion for 10 hours.
    Quantity I: First person speed
    Quantity II: Second person speed
    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 or relation cannot be established
    
    Answer & Explanation

    B. Quantity I < Quantity II
    Explanation:
    First person speed = 25 m/s * 18/5 = 90 kmph
    Second person speed = 35 m/s * 18/5 = 126 kmph