# SBI Clerk Pre Quantitative Aptitude (Day-21)

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Inequality

Directions (Q. 1 – 10): Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give answer as,

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

1) Quantity I: If the ratio of the length of the rectangle to the side of the square is 5 : 8 and the ratio of the breadth of the rectangle to the side of the square is 1: 2. If the difference between the perimeter of the rectangle and the square is 56 cm, then what is the area of the rectangle?

Quantity II: If the radius of the sphere is 4.9 cm, what is the surface area of the sphere?

2) Quantity I: If the shopkeeper sold the article for Rs. 1200 and he earned X% of the profit. If he increase the selling price of the article by Rs. 300 and he can makes the profit of (X + 30) %, then find the value of X?

Quantity II: If the marked price of the article is Rs.2800 and the Shopkeeper offers X % of discount. If he sold at the article at Rs.2400, then find the value of X?

3) Quantity I: A milkman has 72 litres of mixture of water and milk in the ratio of 4: 5. Then he adding some amount of water and the volume of the mixture is increased by 88 liters. The quantity of the milk is how much percentage more or less than of water in the final mixture?

Quantity II: 15 %

4) Quantity I: Ratio of the number of red, blue and yellow balls in the box is 4: 3: 5. If 18 yellow balls taken out and 10 blue balls is added, then the ratio of red, blue and yellow balls become 6: 7: 3. What is the total number of balls in the box at initially?

Quantity II: The income of A is Rs. 80000 and he spends Rs. 32000 and save the remaining amount. What percent of salary he saves?

5) Quantity I: The ratio of income of A and B is 4: 5. The sum of their expenditures is Rs. 40000 and the amount of the savings of A is equal to the expenditure of B. Find the ratio of their incomes to the sum of their savings?

Quantity II: A and B shared a profit in the ratio of 5: 4. They invested for 7 months and 8 months respectively. Then find the ratio of their investments?

6) Quantity I: The sum Rs. 1200 invested at same rate of interest in simple and compound interest scheme and the difference between the interests is Rs. 27 for 2 years. Find the rate of interest?

Quantity II: What is the rate of interest on the amount Rs. 2000 invests in the compound interest scheme for 2 years and the amount obtained after 2 years is Rs. 2645?

7) Quantity I: A car covered a distance of 210 km in 14 hours. Ratio of the speed of bike to speed of the car is 4: 3. In how much distance will the bike cover in 3 hours?

Quantity II: A man goes from his house to office at the speed of 20 kmph and reaches the office at 15 minutes late. If he increases his speed by 5 kmph and reaches the office in time, then what is the distance between house and office?

8) Quantity I: 600 m length of train A crosses train B running in opposite direction in 36 seconds and train A also crosses a man standing in a platform in 36 seconds. What is the speed of train B if the length of train B is half of train A?

Quantity II: A train crosses an electric pole in 18 seconds and crosses 125 m long tunnel in 36 seconds. What is the speed of the train?

9) Quantity I: Pipe A can fill the tank in 20 hours and ratio of the efficiency of pipe A to B is 3: 2. Pipe B and pipe C together can fill the tank in 15 hours. In how many hour pipe A, B and pipe C together can fill the tank?

Quantity II: Pipe A can fill the tank in 30 hours and Pipe B can fill the tank in 15 hours. In what time will the tank is completely fill, if both the pipes are opened together?

10) Quantity I: Ratio of the ages of A and B is 4: 5 and after 4 years the age of C is 22 years. If the average ages of A, B and C is 15 years, then what is the present age of B?

Quantity II: If the sum of the ages of A and B is 45 years and the ratio of the ages of A to B after 21 years is 17: 12, then what is the present age of B?

Directions (1-10) :

From quantity I,

Ratio of length of rectangle to side of the square = 5: 8

Ratio of the breadth of the rectangle to side of the square = 1: 2

Ratio of the length and breadth of the rectangle and side of the square = 5: 4: 8

Perimeter of the rectangle = 2 * (l + b) = 2 * (9x) = 18x

Perimeter of the square = 4 * a = 4 * 8x = 32x

32x – 18x = 56

x = 4 cm

Area of the rectangle = l * b

= (5 * 4) * (4 * 4)

= 320 cm2

From quantity II,

Radius of the sphere = 4.9 cm

Surface area of the square = 4 * 22/7 * r * r

= 4 * 22/7 * 4.9 * 4.9 = 301.84 cm2

Quantity I > Quantity II

From quantity I,

CP * (X + 100)/100 = 1200

CP * (X + 130)/100 = 1500

120000/(X + 100) = 150000/(X + 130)

4X + 520 = 5X + 500

X = 20 %

From quantity II,

2800 * (100 – X)/100 = 2400

100 – X = 600/7

X = 100/7

X = 14.28 %

Quantity I > Quantity II

From Quantity I:

Milk = 5/9 * 72 = 40

Water = 4/9 * 72 = 32

Added water quantity = 88 – 72 = 16

Total quantity of water = 16 + 32 = 48

Required percentage = [(48 – 40)/48] * 100 = 16.67 %

From Quantity II:

Quantity II = 15 %

Quantity I > Quantity II

From quantity I,

Ratio of the red, blue and yellow balls = 4: 3: 5

(5x – 18)/(3x + 10) = 3/7

9x + 30 = 35x – 126

26x = 156

X = 6

Total number of balls = 12x = 12 * 6 = 72

From quantity II,

Income = 80000

Expenditure = 32000

Savings = 80000 – 32000 = 48000

Required percentage = 48000/80000 * 100 = 60 %

Quantity I > Quantity II

Quantity I:

Income                Expenditure        Savings

A        4x                         y                         4x – y

B        5x                         4x – y                  5x – (4x – y) = x + y

Required ratio = (4x + 5x): (4x – y + x + y)

= > 9x : 5x = 9 : 5

= > (9/5) = 1.8

Quantity II:

Investment ratio * Period ratio = Ratio of profit

Ratio of investment = Ratio of profit / Period ratio

= > (5 / 7) : (4 / 8)

= > 10 : 7

= > (10/7) = 1.428

Quantity I > Quantity II

From quantity I,

Difference = P * R * R / 100 * 100

27 = 1200 * R * R / 100 * 100

Rate of interest = 15%

From quantity II,

CA = P * (1 + R/100)n

2645 = 2000 * (1 + R/100)2

529/400 = (1 + R/100)2

23/20 = (100 + R)/100

115 = 100 + R

R=15%

Quantity I = Quantity II

From Quantity I,

Speed of car = 210/14 = 15 kmph

Speed of bike = 4/3 * 15 = 20 kmph

Distance covered by bike = 20 * 3 = 60 km

From Quantity II,

Distance = (20 * 25 * 15/60)/5

= 25 km

Quantity I > Quantity II

From quantity I,

Speed of train A = 600/36 * 18/5

= 60 kmph

(Speed of train B + 60) * 5/18 = 900/36

Speed of train B = 30 kmph

From quantity II,

Length of train = x

Speed of train = y

x = y * 5/18 * 18

x = 5y

(x + 125) = y * 5/18 * 36

x + 125 = 10y

5y + 125 = 10y

y = 25 kmph

Quantity I > Quantity II

From quantity I,

A = 1/20

B = 3/2 * 20 = 30 hours

B + C = 1/15

C = 1/15 – 1/30

C = 1/30

A + B + C = 1/20 + 1/30 + 1/30

= (3 + 2 + 2)/60

= 7/60

Required time = 60/7 hours

From quantity II,

Required time = 1/30 + 1/15

= 3/30 = 1/10

= 10 hours

Quantity I < Quantity II

From quantity I,

C’s present age = 22 – 4 = 18 years

9x + 18 = 15 * 3

9x = 27

x = 3 years

B’s present age = 5 * 3 = 15 years

From quantity II,

A + B = 45

Sum of the ages of A and B after 21 years = 45 + 21 + 21 = 87 years

B’s age after 21 years = 12/29 * 87 = 36 years

B’s present age = 36 – 21 = 15 years

Quantity I = Quantity II

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