Quantitative Aptitude: Inequalities Set 1

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. If x and y are natural numbers and 5 > x > y > 0.
   Quantity I: 3x²y
   Quantity II: 4xy²
   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 B
   Explanation:
   Divide both equations. So
   I/II = 3x/4y
   Or I = 3x/4y * II
   Now y has to be > 0 and x has to be > y
   If x = 2, y = 1, I > II
   If x = 3, y = 1, I > II
   Similarly we will get I > II in all cases
   Now x has to be < 5,
   So check If x = 4, y = 3, then I = II
   So final we get I ≥ II
2. A and B started a business with Rs 10,000 and Rs 15,000 respectively. After 6 months C joined them with Rs 20,000.
   Quantity I: B′s share in total profit of Rs 4,00,000 at the end of 2 years.
   Quantity II: Annual Salary of Rohit after tax deduction if he earns Rs 20,000 per month and pays a tax of 20% each month.
   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
   Explanation:
   I: A:B:C = 10000*24 : 15000*24 : 20000*18=2:3:3
   B=3/8 *4,00,000= Rs 1,50,000
   II: Salary after deducation = 20,000*12*80/100 = Rs 1,92,000
   Hence I < II
3. A can do a work in 16 days. B is 60% more efficient than A.
   Quantity I: Time taken by A and B together to do the work.
   Quantity II: Time taken by A and B to do the work together when A works at double his original efficiency and B works at half his original efficiency.
   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
   Explanation:
   I: A=16 days ; B = 16 * 100/160=10 days
   A+B together = 16*10/(26)=80/13 days
   II: A = 16 days ; B = 10 days
   A(double efficiency) = 8 days ; B(half efficiency) = 20 days
   A+B together = 80/14
   hence I > II
4. The value of a machine depreciates at 10% per annum
   Quantity I: Value of machine after 2 years, if the present value of machine is Rs 96000
   Quantity II: Distance travelled by a taxi in 1 year, if it travels at a constant speed of 40kmph and covers 213 kilometers everyday.
   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
   Explanation:
   Value of machine after 2 years = 96000*90/100*90/100= Rs 77,760
   II: Here we do not need speed, as we can find the total distance travelled by the everyday distance.
   If the year is leap year then total distance travelled = 213*366= 77,958 km
   if non leap year then =213*365 = 77,745 km
   hence relation cannot be established.
5. A rectangular plot measuring 80 meters by 40 meters is to be enclosed by wire fencing along the boundary of the plot. The fence will be tied on poles that will be placed along the boundary.
   Quantity I: Number of poles required for fencing if each pole is at a distance of 24 meters.
   Quantity II: Radius of a circle whose area is 10% of the area of the rectangular plot.
   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
   Explanation:
   I: Perimeter= 2(80+40)=240
   No. of poles = 240/24=10
   II: Area of circle = 320 =>22/7*r*r=320
   r=101.81 => r >10
   Hence II > I
6. A bag contains 3 red, 4 green and 2 blue balls. Two balls are drawn at random.
   Quantity I: Probability that None of the ball drawn is blue.
   Quantity II: Fraction of work completed by A in 7 days if he is 20% more efficient than B who can complete the work in 12 days.
   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
   Explanation:
   I: 7C2/9C2=7/12
   II: A-> 10 days => fraction of work in 7 days = 7/10
   Hence II > I
7. Suresh took a loan from bank at 12% p.a simple interest. After 3 years he had to pay back Rs. 16,200 as interest.
   Quantity I: Loan taken by Suresh from the bank.
   Quantity II: Amount after 2 years for a principal of Rs 35,000 at interest rate of 10% compounded annually.
   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
   Explanation:
   I: P=16200*100/(3*12)=Rs 45,000
   II: A= 35000*121/100=Rs 42,350
   Hence I > II
8. A man can row 9 kmph in still water. It takes him twice as long to row up as to row down the river.
   Quantity I: Rate of stream.
   Quantity II: Speed of a man in still water who can row upstream at 4 kmph and downstream at 2 kmph.
   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
   Explanation:
   I: 9+y=2(9-y)
   y = 3 kmph
   II: x = (4+2)/2=3 kmph
   Hence I = II
9. A man can row at a speed of 8 kmph in still water to a certain upstream point and back to the starting point in a river flowing at 4 kmph.
   Quantity I: Average speed of man for the total journey.
   Quantity II: Speed of a cyclist, cycling in a circular ground of radius 7 kilometer if he takes 4 hour to complete one full round of the ground.
   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
   Explanation:
   I: Average Speed = U * D/x
   U = (8+4) = 12 ; D = (8 – 4) = 4
   Avg Speed = 12 * 4/8 = 6 kmph
   II: Distance(Circumference) = 2*π*r = 44 km ; Time = 4 hours
   Speed = 44/4 = 11 kmph
   hence II > I
10. A train 175 meter long passes a man moving at 6 kmph in the same direction in which the train is going, in 10 seconds.
    Quantity I: Speed of the train.
    Quantity II: Average speed of a car going from point A to B at 65 kmph and back from point B to A at 70 kmph.
    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
    Explanation:
    I: Relative speed = 175/10 m/s = (175/10)*(18/5) = 63 kmph
    Let speed of train = x kmph => relative speed = x-6
    x – 6 = 63
    => x = 69 kmph
    II: Avg speed = (2*65*70)/(65+70) = 67.40 kmph
    Hence I > II