BANK & INSURANCE (QUANTITY COMPARISION)

Total Questions: 100

1. Two Statement Based Questions

Directions (1-5): In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered)

Ques:

Quantity I: Anil, Yashika and Rani together can complete the piece of work in 48 days. Anil and Rani together can complete the work in 72 days and Yashika and Rani together can complete the work in 96 days. In how many days Rani alone can complete the work?

Quantity II: Pipe A and B together can fill the tank in 32 hours and 64 hours respectively. If pipe A and B opened together and after 12 hours pipe B is closed, in how many hours required to fill the tank completely?

Correct Answer: (a) Quantity I > Quantity II
Solution:

From quantity I,
Anil, Yashika and Rani together can complete the piece of work in 48 days. Anil and Rani together can complete the work in 72 days,
Yashika and Rani together can complete the work in 96 days,

Total work is LCM of (48,72,96) = 576 units
Efficiency of Anil, yashika and rani = 576/48
= 12 units/day
Efficiency of Anil and rani = 576/72 = 8 units/day
Efficiency of yashika and rani = 576/96
= 6 units/day
Individual efficiency of anil, yashika and rani
= 6 : 4 : 2
Rani can complete the work = 576/2 = 288 days

From quantity II,
Pipe A and B together can fill the tank in 32 hours and 64 hours

Total capacity is LCM of (32, 64) = 64 litres
Efficiency of Pipe A = 64/32 = 2 litres/hr
Efficiency of Pipe B = 64/64 = 1 litres/hr

Let the tank is filled in X hours X×2 + 12×1 = 64
X = 26

So, the tank is filled in 26 hours.
Therefore, Quantity I > Quantity II

2. Amal alone completes the work in 30 days and the efficiency of Amal is 3/2 of the efficiency of Bala.

Quantity I: If the ratio of the efficiency of Bala and Prabu is 4:3, in how many days Amal, Bala and Prabu together can complete the work?

Quantity II: Bala and Paul together can complete the work in 30 days. In how many days Paul alone can complete the whole work?

Correct Answer: (c) Quantity II > Quantity I
Solution:

From quantity I,
One day work of Amal = 1/30
One day work of Bala = 1/30 × 2/3 = 1/45
One day work of Prabu = 1/45 × 3/4 = 1/60

1/A + 1/B + 1/C
= 1/30 + 1/45 + 1/60
= (6 + 4 + 3)/180
= 13/180

Required time taken by all of them together
= 180/13 days

From quantity II,
One day work of Amal = 1/30
One day work of Bala = 1/30 × 2/3 = 1/45
One day work of paul’s = 1/30 - 1/45 = 1/90

Paul can complete the work = 90 days

Therefore, Quantity I < quantity II

3. Quantity I: Train A crosses train B running in the opposite direction in 15 seconds and also crosses a man standing on a platform in 18 seconds. If the length of train A is 50% more than that of train B and the speed of train B is 60 kmph, then find the length of train A?

Quantity II: Train A crosses a car running in the opposite direction at the speed of 45 kmph in 13.5 seconds and the speed of train A is 75 kmph. Find the length of train A?

Correct Answer: (c) Quantity II > Quantity I
Solution:

From quantity I,
Let take, Length of train B = 2x
Length of train A = 2x × 150/100 = 3x
Speed of train A = y
Speed = Length/Time
Y = 3x/18
3x = y × 5/18 × 18
3x = 5y

3x + 2x = (y + 60) × 5/18 × 15
30x = 25y + 60 × 25
30x = 15x + 60 × 25
x = 100
Length of train A = 3 × 100 = 300 m

From quantity II,
Speed of the car = 45 km/hr and speed of the train = 75 km/hr
Length = Speed × Time
Length of train A = (75 + 45) × 5/18 × 13.5
Length of train A = 450 m
Therefore, Quantity I < quantity II

4. Quantity I: The age of Vimal after 7 years is 25 years and the ratio of the ages of Vibin and Bibin is 7:3. If the ratio of the age of Vimal and Vibin after 9 years is 9:10, then find the present age of Bibin?

Quantity II: If the circumference of the circle is 176 cm, and the radius of the cylinder is half of the radius of the circle and the volume of the cylinder is 5544 cm³, then find the height of the cylinder?

Correct Answer: (e) Quantity I = Quantity II or Relation cannot be established
Solution:

From quantity I,
Vimal's age after 7 years = 25 years
Vimal present age = 25 – 7 = 18 years
Vibin age after 9 years = 10/9 × (18 + 9) = 30 years
Present age of bibin = 3/7 × (30 – 9) = 9 years

From quantity II,
Circumference of the circle = 176 cm
Circumference of the circle = 2πr = 2 × 22/7 × r
= 176 r = 28 cm
Radius of the cylinder = 28/2 = 14 cm
Area of a cylinder = πr²h = 22/7 × 14 × 14 × h
= 5544
Height of the cylinder = 9 cm

Therefore, Quantity I = quantity II

5. Quantity I: The average weight of the class is 64 kg and the average weight of the boys in the class is 72 kg. If the number of girls in the class is 25% more than the number of boys in that class and the total number of students in the class is 72, then find the average weight of the girls in the class?

Quantity II: 52 kg

Correct Answer: (a) Quantity I > Quantity II
Solution:

From quantity I,
Ratio of number of boys to girls = 100:125 = 4:5
Number of boys = 72 × 4/9 = 32
Number of girls = 72 × 5/9 = 40
Total weight of the class = 64 × 72 = 4608
Average weight of the girls = (4608 – 32 × 72)/40
= 57.6 kg

Quantity II: 52 kg
Therefore, Quantity I > quantity II

6. Directions (6-10): In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered)

Quantity I: The shopkeeper sold some apples to Rahul at the rate of 20 apples for Rs.60 and Rahul sold the same apples to Sam at the rate of 50 apples for Rs.300. What is the profit earned by Rahul?

Quantity II: A shopkeeper sold some apples and he sold 25% of the total apples at 20% profit, two fifth of the total apples at 25% profit and sold the remaining apples at 20% profit. What is the overall profit or loss percentage to the shopkeeper?

Correct Answer: (a) Quantity I > Quantity II
Solution:

From quantity I,
Cost price of the apples to Rahul = 60/20 = Rs.3 per apple
Selling price of the apples by rahul to Sam = 300/50
= Rs.6 per apple
Required percentage = [(6 – 3)/3] × 100 = 100%

From quantity II,
Let the total number of apples = 100
Let Cost price per apple = Rs.10
Profit on First part = 100 × 25/100 × 10 × 20/100
= Rs.50
Profit on Second part = 100 × 2/5 × 10 × 25/100
= Rs.100
Profit on Remaining part = 35 × 10 × 20/100 = Rs.70
Total profit = 50 + 100 + 70 = Rs.220
Required percentage = 220/1000 × 100 = 22%
Therefore, Quantity I > Quantity II

7. Quantity I: A and B started the business with an investment ratio of 4:5 respectively. At the end of one year, 25% of the total profit goes to insurance and A’s profit share is Rs.300, what is the total profit earned by them?

Quantity II: A and B started the business with the investment of Rs.x and Rs.(x + 500) respectively. At the end of one year, the total profit is Rs.3400 and B’s profit share is Rs.2200. What is B’s initial investment?

Correct Answer: (c) Quantity II > Quantity I
Solution:

From quantity I,
Profit ratio of A and B = 4:5
A’s share = Rs.300
25% of the profit goes to insurance.
4/9 × 3/4 × (Total profit) = Rs.300
Total profit received by A and B together = Rs.900

From quantity II,
Investment ratio of A and B = x : (x + 500)
Profit ratio of A and B = 1200 : 2200
(x + 500)/(2x + 500) = 2200/3400
22x + 5500 = 17x + 8500
5x = 3000
x = 600
B’s initial investment = 600 + 500 = Rs.1100
Therefore, Quantity I < Quantity II

8. Quantity I: The ratio of the milk and water in the mixture is 4:3. If in 35 litres of the mixture, 10 litres of water is added, then what is the percentage of water in the final mixture?

Quantity II: In 2017 number of employees in the company is 2800 and the number of employees in 2019 is 4500. What is the approximate percentage increase in the number of employees from 2017 to 2019?

Correct Answer: (c) Quantity II > Quantity I
Solution:

From quantity I,
Initial mixture = 35 litres
Ratio of milk and water = 4 : 3
Milk in the mixture = 4/7 × 35 = 20 litres
Water in the mixture = 3/7 × 35 = 15 litres
After adding 10 litres of water, then quantity of water in the new mixture = 15 + 10 = 25 litres
New mixture of milk and water = 35 + 10 = 45 litres
Required percentage = 25/45 × 100 = 55.56%

From quantity II,
Number of employees in the year 2017 = 2800
Number of employees in the year 2019 = 4500
Required percentage = [(4500 – 2800)/2800] × 100 = 60.71%

Therefore, Quantity I < Quantity II

9. Quantity I: The ratio of the present age of A and B is 3:8 respectively and after 4 years B’s age is twice of A’s age after 9 years. What is the present age of A?

Quantity II: If the Product of the ages of A and B is 437 and after 6 years A’s age is 25 years, then what is the present age of B?

Correct Answer: (c) Quantity II > Quantity I
Solution:

From quantity I,
Ratio of present age of A and B = 3:8
(8x + 4) = 2 × (3x + 9)
8x + 4 = 6x + 18
2x = 14
x = 7
A’s present age = 3 × 7 = 21 years

From quantity II,
Product of the ages of A × B = 437 years
A’s age + 6 years = 25 years
Present age of A = 19 years
B’s present age = 437/19 = 23 years

Therefore, Quantity I < Quantity II

10. Quantity I: A and B started the business with the investment in the ratio of 3:2 respectively. If at the end of one year, A’s profit share is Rs.4800, then what is B’s profit share?

Quantity II: A and B started the business with investments of Rs.2400 and Rs.x respectively. At the end of one year, the total profit is Rs.9000 and A’s profit share is Rs.4000. Find the value of x?

Correct Answer: (a) Quantity I > Quantity II
Solution:

From quantity I,
Investment ratio of A and B = 3:2
Time ratio of A and B = 12 : 12
Profit ratio of A and B = 3×12 : 2×12 = 3 : 2
A’s profit share = Rs.4800
B’s profit share = 4800 × 2/3 = Rs.3200

From quantity II,
Investment ratio of A and B = 2400 : x
Time ratio of A and B = 12 : 12
Profit ratio of A and B = 2400×12 : x×12 = 2400 : x
B’s profit = 9000 – 4000 = Rs.5000
2400/x = 4000/5000
4x = 5 × 2400
x = 3000
Investment of B = Rs.3000

Therefore, Quantity I > quantity II