# Quantitative Aptitude: Inequalities Set 11 (For Mains Exams)

Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give answer.

1. A and B started a business with Rs.10000 and Rs.15000 respectively. After 6 months C joined them with Rs.20000.

Quantity I: B′s share in total profit of Rs.4,00,000 at the end of 2 years.

Quantity II: Annual Salary of Druv after tax deduction if he earns Rs.20,000 per month and pays a tax of 20% each month.

Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I = Quantity II
Option A
Quantity I: A: B: C = 10000*24 : 15000*24 : 20000*18=2:3:3

B=3/8 *400,000= Rs.150000

Quantity II: Salary after deduction = 20,000*12*80/100 = Rs.192000
Hence, Quantity I < Quantity II

2. Lalith can do a work in 16 days. Arul is 60% more efficient than Lalith.
Quantity I: Time taken by Lalith and Arul together to do the work.

Quantity II: Time taken by Lalith and Arul to do the work together when Lalith works at doubles his original efficiency and Arul works at half his original efficiency.

Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I = Quantity II
Option C
Quantity I: Lalith =16 days; Arul= 16 * 100/160=10 days

Lalith+arul together = 16*10/(26)=80/13 days

Quantity II: Lalith = 16 days; Arul = 10 days

Lalith (double efficiency) = 8 day; Arul (half efficiency) = 20 days

Lalith+Arul together = 80/14
Hence, Quantity I > Quantity II

3. A bag contains 3 Yellow, 4 black and 2 white balls. Two balls are drawn at random.

Quantity I: Probability that none of the flowers drawn is white.

Quantity II: Fraction of work completed by Thanu in 7 days if she is 20% more efficient than Meenu who can complete the work in 12 days.

Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I = Quantity II
Option A
Quantity I: 7C2/9C2=7/12

Quantity II: Meenu-> 10 days => fraction of work in 7 days = 7/10

Hence, Quantity I < Quantity II

4. The Person took a loan from bank at 12% P.A. simple interest. After 3 years he had to pay back Rs.16200 as interest.

Quantity I: Loan taken by person from the bank.

Quantity II: Amount after 2 years for a principal of Rs.35,000 at interest rate of 10% compounded annually.

Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I = Quantity II
Option C
Quantity I: P=16200*100/(3*12)=Rs.45,000

Quantity II: A= 35000*121/100=Rs.42350

Hence, Quantity I > Quantity II

5. A fisherman can row 9Kmph 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 person in still water who can row upstream at 4kmph and downstream at 2kmph.

Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I = Quantity II
Option E
Quantity I: 9+y=2(9-y)

y = 3kmph

Quantity II: x = (4+2)/2=3kmph

Hence Quantity I = Quantity II

6. Quantity I: Train A crosses the pole in 28 sec at the speed of 90 kmph.

Quantity II: Train B crosses the 500 m platform in 54 sec at the speed of 108 kmph.

Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I = Quantity II
Option A

Distance = speed * time

Quantity I:

Let the length of train A be x,

Then,

x = 90 * 5/18 * 28

x = 700 m

Quantity II:

Let the length of train B be x,

Then,

500 + x = 108 * 5/18 * 54

500 + x = 1620

x = 1120

Quantity I > Quantity II

7. Quantity I: The Simple interest on that sum at the rate of 20 % per annum for 2 years is Rs. 1000.

Quantity II: Rs. 2500

Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I = Quantity II
Option E
Quantity I:

SI = pnr/100

1000= p * 20/100 * 2

p = Rs. 2500

Quantity II: Rs. 2500

Quantity I = Quantity II

8. Quantity I: If the ratio of ages of Vishnu and Thaja, 5 years ago is 10: 16 and difference of their age is 30 years, then find the sum of the present age of Varun and Tharun?

Quantity II: If the average age of A, B, C and D is 40 years, then find the sum of the ages of all of them?

Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I = Quantity II
Option C
Quantity I:

The ratio of ages of Vishnu and Thaja, 5 years ago = 10: 16 (10x, 16x)

16x – 10x = 30

x = 5

Required sum = 16x + 10 = (16 * 5) + 10 = 90 years

Quantity II:

Required sum = 40 * 4 = 160 years

Quantity I < Quantity II

9. Quantity I: A bag contains 3 orange balls and 4 blue balls. If one ball is taken out randomly, then find the probability of selecting the ball of blue color.

Quantity II: A bag contains 3 lime balls and 4 yellow balls. If one ball is taken out randomly, then find the probability of selecting the ball of lime color.

Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I = Quantity II
Option A
Quantity I:

Required probability = 4C1 / 7C1 = 4/7

Quantity II:

Required probability = 3C1 / 7C1 = 3/7

Quantity I > Quantity II

10. Quantity I: Find the volume of the sphere, whose radius is 10.5 cm.

Quantity II: Find the volume of the cone whose height and diameter is 3.5 cm and 16 cm respectively?

Quantity I > Quantity II
Quantity I >= Quantity II
Quantity I < Quantity II
Quantity I <= Quantity II
Quantity I = Quantity II
Option A
Quantity I:

Volume of the sphere = (4/3)*πr3 = 4/3 * 22/7 * 10.5 * 10.5 * 10.5 = 4851 cm3

Quantity II:

Volume of the cone = (1/3)*πr2h = 1/3 * 22/7 * 16/2 * 16/2 * 3.5 = 234.66 cm3

Quantity I > Quantity II