Quantitative Aptitude: Inequalities Set 2 (New Pattern)

Directions: Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly.

  1. The price of item X is marked at Rs 10,000. After giving a discount of 4%, a gain of 20% is achieved.
    Quantity I: Cost Price of Item X.
    Quantity II:  Selling Price of item Y after two successive discount of 10% and 15% is provided on the Marked Price of Rs 10,000.
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option A
    Solution:  
     I : Mp =Rs 10,000; SP after 4% discount = Rs 9600; CP = Rs 8000
    II : SP= 10,000*90/100 * 85/100 = Rs 7650
    Hence I > II 
  2. Quantity I: Simple Interest on a sum of Rs 6200 at the rate of 6% per annum for 5 years
    Quantity II:  Compound Interest on a sum of Rs 6400 at rate of 10% compounded semi-annually for one year.
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option A
    Solution:  
     I: SI = 6200*6*5/100 = Rs 1860
    II: CI = 6400 [1 – 5/100]<sup>2</sup> – 6400 = Rs 1376
    Hence I > II 
  3. The price of item X is marked at Rs 10,000. After giving a discount of 4%, a gain of 20% is achieved.
    Quantity I: Cost Price of an article if it is sold making a loss of 10% given that if the cost price was 20% less, a profit of Rs 12 could be made.
    Quantity II:  Labeled Price of an article if a discount of 30% is given on it and then sold for  Rs 105 at a loss of 20%
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option E
    Solution:  
     I: Let CP = Rs 100, then at 10% loss, SP = Rs 90
    Now if CP is 20% less, means CP = Rs 80, then profit is = 90 – 80 = Rs 10
    but given profit is Rs 12
    So if profit is Rs 10, then CP = Rs100
    If profit is Rs 12, then CP is 100/10 * 12 = Rs 120
    II: Use formula MP = (100-loss%)/(100-dicount%) * CPS
    So MP = (100-20)/(100-30) * 105 = Rs 120
    Hence I = II 
  4. Given that x < 0 and y > 0
    Quantity I: 14x3y2
    Quantity II:  28x2y3
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option C
    Solution:  
     I: Since x < 0, so I will always be negative
    II: It will be always positive
    Hence I < II 
  5. Quantity I: Area of rectangle whose sides are in the ratio 3 : 1 and perimeter twice the circumference of a semi-circle with area 77 cm<sup>2</sup>
    Quantity II:  Curved surface area of a cylinder of radius 12 cm and height equal to the side of square of area 49cm<sup>2</sup>
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option C
    Solution:  
     I: ½ πr<sup>2</sup> = 77 [area of semicircle]
    So r = 7 cm
    So circumference of semicircle  = πr = 22 cm
    So perimeter of rectangle = 2*22 = 44 cm
    So 3x+x = 44 cm, x = 11,
    So area of rectangle = 3x<sup>2<sup> = 363cm<sup>2</sup>
    II: height of cylinder = √49 = 7 cm
    So CSA = 2πrh = 528cm<sup>2</sup>
    Hence I < II 
  6. Quantity I: Time taken by A to complete 1/5th of work if B takes 6 days to complete 3/5th of work and together they take 5 days to complete 3/4th of work
    Quantity II:  Time taken by a train to cross a platform of length 60 km given that it crosses a pole in two and a half hours running at 60 km/hr
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option A
    Solution:  
     I: A and B completes 3/4th work in 5 days, so complete 1 work in 4/3 * 5 = 20/3 days
    B complete 3/5 work in 6 days, so complete work in 5/3 * 6  = 10 days
    So in 1 day A completes = 3/20 – 1/10 = 1/20
    So to complete 1/5th work = 1/5 * 20 = 4 days
    II: length of train = 2.5 * 60 = 150 km
    So time taken to cross platform of length 60 km with speed 60 km/hr = (150+60)/60 = 3.5 hrs
    Hence I > II 
  7. Quantity I: Age of A five years ago if 6 years hence ratio of age of A to B will be 14 : 11, and 1 year ago the ratio was 7 : 5.
    Quantity II:  Average age of 2 students included in a group of 5 students with average age 18 years given that addition of these 2 students in group makes average increase by 1.
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option C
    Solution:  
     I: (A+6)/(B+6) = 14/11
    And (A-1)/(B-1) = 7/5
    Solve the equations, A = 22, so 5 years ago = 22 – 5 = 17 years
    II: Total age of 2 students added to group = 18*2 + 7*1 = 43
    So their average age = 43/2 = 21.5 years
    Hence I < II 
  8. Quantity I: x, such that 6x2 + 22x + 15 = 0
    Quantity II:  y, such that 6y2 – 7y – 10 = 0
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option D
    Solution:  
     I: x = -3, -5/6
    II: y= -5/6, 2
    Hence I ≤ II 
  9. A shopkeeper gets a discount of 20% on an article and sells it at 10% profit.
    Quantity I: Labeled price as a percent of cost price.
    Quantity II:  Profit percent if discount given is 60%
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option C
    Solution:  
     I: MP = (100+10)/(100-20) * CP = 11/8 of CP
    So required % = MP/CP * 100 = (11CP/8)/CP * 100 = 137.5%
    II: % profit = (100+10) [(100-10)/(100-60)] – 100 = 590/4 = 147.5%
    Hence I < II 
  10. Quantity I: Speed of boat in still water f it took 24 hours to cover a distance of 64 km going downstream and back. Given the speed of current to be 2 km/hr
    Quantity II:  Average speed of a boy to go from home to school if his average speed is 2 km/hr from school to home and he covers a total of 12 km in 5 hours.
    A) Quantity I > Quantity II
    B) Quantity I ≥  Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥  Quantity I
    E) Quantity I = Quantity II or Relation cannot be established
    View Answer
       Option A
    Solution:  
     I: Let speed of boat = x km/hr
    So 64/(x+2) + 64/(x-2) = 24
    Solve, x = 6 km/hr
     II : Distance from home to school is 12/2 = 6 km
    Let speed from home to school is x km/hr
    So using distance = total time * average speed
    6 = 5 *[2*x/(2+x)]
    Solve, x = 3 km/hr
    Hence I > II 

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4 Thoughts to “Quantitative Aptitude: Inequalities Set 2 (New Pattern)”

  1. ^^^Jaga^^^....

    no 10 ka quantity ii without formula kese hoga?

    1. Total time 5 hrs hai jisse break nhi kar sakte so use T = d/s
      So
      5 = 6/2 + 6/x
      X = 3

      1. ^^^Jaga^^^....

        thank u mam

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