# SBI PO Prelims Quantitative Aptitude Question Paper 2019

• Last Updated : 28 Mar, 2022

#### Direction (1-5): The following questions contain two equations as I and II. You have to solve both the questions and determine the relationship between them and give answers as,

• A)  x > y
• B)  x ≥ y
• C)  x < y
• D)  x ≤ y
• E)  x = y or the relation cannot establish.

#### 1. Question

I) x2 – 10x – 24 = 0

II) y2 + 16y – 36 = 0

Solution:

x2 – 10x – 24 = 0

x2 – 12x + 2x – 24 = 0

(x – 12) (x + 2) = 0

x = 12 , – 2

y2 + 16y – 36 = 0

y2 + 18y – 2y – 36 = 0

(y + 18)( y – 2)= 0

y= 2 , -18

Thus, the relationship can not be established between x and y.

#### 2. Question

I) x – (256)1/4 = 0

II) y2 + (125)1/3 = 21

Solution:

x – (256)1/4 = 0

x = (256)1/4

x = 4

y2 + (125)1/3 = 21

y2 + 5 = 21

y2 = 16

y = +4, -4

Thus, x is either greater than or equal to y.

#### 3. Question

I) x2 – 5x -14 = 0

II) y2 + 9y + 20 = 0

Solution :-

x2 – 5x -14 = 0

x2 – 7x + 2x – 14 = 0

(x – 7) (x + 2) =0

x = 7, -2

y2 + 9y + 20 = 0

y2 + 5y + 4y + 20 = 0

(y + 4) (y + 5) = 0

y =  -4, -5

Thus, x is greater than y.

#### 4. Question

I) 10x2 – 3x – 1 = 0

II) y2 + 5y = – 6

Solution:

10x2 – 3x – 1 = 0

10x2 – 5x + 2x – 1 = 0

5x(2x – 1) + 1(2x – 1) = 0

(2x – 1) (5x + 1) = 0

x = 1/2 , -1/5

y2 + 5y + 6 = 0

y2 + 2y + 3y + 6 = 0

y(y + 2) + 3 (y + 2) = 0

(y + 2)(y + 3) = 0

y =  -3 ,  -2

x > y

Thus, x is greater than y.

#### 5. Question

I) x2 + 17x + 42 = 0

II) 2y2 – 15y + 22 = 0

Solution:

x2 + 17x + 42 = 0

x2 + 14x + 3x + 42 = 0

x(x + 14) + 3 (x + 14) = 0

(x + 14) (x + 3) = 0

x = -14 , – 3

2y2 – 15y + 22 = 0

2y2 – 11y – 4y + 22 = 0

y (2y – 11) – 2(2y – 11) = 0

(y – 2) (y – 11) = 0

y =  2, 11/2

x < y

Thus, y is greater than x.

#### 6. Question

5, 30, 150, 600, ?

a) 1500

b) 1200

c) 1300

d) 1800

e) 2000

Solution:

5 * 6 = 30

30 * 5 = 150

150 * 4 = 600

600 * 3 = 1800

Thus, the number is 1800.

#### 7. Question

104, ?, 96, 120, 88, 128

a) 108

b) 112

c) 120

d) 96

e) 100

Solution:

104 + 8 = 112

112 – 16 = 96

96 + 24 = 120

120 – 32 = 88

88 + 40 = 128

Thus, the number is 112.

#### 8. Question

15, 8, 9, 15, 32, ?

a) 60

b) 72

c) 82.5

d) 80

e) 96

Solution:

15 * 0.5 + 0.5 = 8

8 * 1 + 1 = 9

9 * 1.5 + 1.5 = 15

15 * 2 + 2 = 32

32 * 2.5 + 2.5 = 82.5

Thus, the number is 82.5

#### 9. Question

26, 63, 124, 215, ?

a) 315

b) 325

c) 332

d) 326

e) 342

Solution:

63 – 26 = 37

124 – 63 = 61 (Difference b/w 61-37=24)

215 – 124 = 91 ( Difference b/w 91-60=30)

Each time +6 is added so next number is 36 .

It should be added to 91 ,  the sum is = ( 91 + 36) = 127

Again this 127 should be added to 215 ,

Sum is = ( 127 + 215 ) = 342

Thus, the number is 342.

#### 10. Question

200, 197, 185, 163, ?

a) 130

b) 120

c) 150

d) 140

e) 160

Solution:

(200 – 197) = 3

(197 – 185 ) = 12 (Difference b/w 12 – 3 = 9)

(185 – 163 ) = 22 (Difference b/w 22 – 12 = 10)

Each time + 1 added, So the next number should be 10 + 1 = 11

It should be added to 22 ,

(22 + 11)  = 33

this 33 subtracted from 163 ,

( 163 – 33) = 130

Thus, the number is 130.

#### A clerk can able to typing at a certain speed. He increases his typing by 10% per hour in the first two hours, decreases by 10% in the next one hour, remains constant in the next one hour, and again increases by 5% per hour in the next two hours. If the total original typing is 40000, find the approximate word typing at the end of 6 hours.

a) 45000

b) 50000

c) 47200

d) 48025

e) 48050

Solution:

10% = 1/10

5% = 1/20

∴ 480250 ÷ 10 = 48025

∴The word typing (approximately) at the end of 6 hours is 48025.

#### Seven years ago, the age of Amit and the present age of Bala is in the ratio of 3:4. After eight years, the age of Amit and Bala will be in the ratio of 3:2. Find the present age of Bala?

a) 6 years

b) 8 years

c) 4 years

d) 7 years

e) None of these

Solution:

The ratio of age of Amit 7 years ago and the present age of Bala

= 3 : 4 (3x, 4x)

Present age of Amit and Bala = 3x + 7, 4x

According to the question,

(3x + 7 + 8)/(4x + 8) = (3/2)

12x + 6 = 6x + 18

x = 2

Thus, the present age of Bala is = 4x = 8 years

#### A boy is written a set of three numbers in his notebook, the average of the first two numbers is 8, the average of the last two numbers is 9 and the average of the first and last numbers is 10. Find the average of three numbers?

a) 9

b) 10

c) 11

d) 6

e) 7

Solution:

Let the numbers be x, y and z,

The average of first two numbers = 8

(x + y) = 16

The average of last two numbers = 9

(y + z) = 18

The average of first and last numbers = 10

(x + z) = 20

2*(x + y + z) = 16 + 18 + 20 = 54

x + y + z = 27

Required average = (27/3) = 9

Thus, the average of three numbers is = 9.

#### A man is rowing a boat. He is moving a certain distance downstream with thrice speed than upstream. Find out the ratio of the speed of the boat in still water to the speed of the current.

(a) 2:1

(b) 5:1

(c) 7:1

(d) 3:1

(e) None of the above

Solution:

Let speed  boat in still water be x km/hr

speed of current = y km/h

Speed downstream = (x + y) km/hr

Speed upstream = (x – y) km/hr

According to the question,

3(x – y) = (x + y)

2x = 4y

x : y = 2 : 1

Thus, the ratio between the speed of boat in still water and the speed of current is = 2:1

#### A biker took 30 seconds less time to cross a circular ground along its diameter than to cover it along its boundary. If his speed is 36 km/hr, what is the circumference of the circle?

a) 1550 m

b) 1700 m

c) 1100 m

d) 1400 m

e) 1650 m

Solution:

36 km/hr × 5/18 = 10 m/s

Distance = speed × time

= 10 × 30 m

= 300 m

According to the question,

πr – 2r = 15

r(22/7 – 2) = 300

r = 525/2

Circumference = 2πr

= 2 × 22/7 × 525/2

=1650 m

Thus, the circumference of the circle is = 1650 m.

#### Direction (16-20): Read the given information carefully and answer the questions given below.

Three shopkeepers A, B & C sell burgers (veg + non-veg) in Week I. Veg & Non-veg burger sold by A are in the ratio 9:7, veg and non-veg burgers sold by B are in the ratio 3:4. Total burgers sold by C is 108, out of which veg & non-veg burgers of C are in the ratio 7:5. Total burgers sold by A, B & C together is 376. Veg burger sold by A is 20% more than the veg burger sold by B.

#### 16. Question

Find the ratio between the veg burger sold by A and C.

a) 8: 7

b) 1: 2

c) 3: 2

d) 7: 8

e) 5: 6

Solution

(Explanation for 16-20)

Burger sold by C = 108

Veg burger by C = 108/12 * 7 = 63

Non- veg burger by C = 108/ 12 * 5 = 45

Burger sold by A and B = 376 – 108 = 268

Veg : Non-veg burger sold by A = 9: 7 (9y, 7y)

Veg : Non-veg burger sold by B = 3: 4 (3x, 4x)

Veg burger sold by B = 100

Veg burger sold by A = 120

Ratio = 6 : 5

9y/6 × 5 = 7.5y

7.5y/3 × 4 = 10y

A( veg ) : A( non – veg ) : B( veg ) : B( non – veg )

= 9 : 7 : 7.5 : 10

= 18: 14: 15: 20

268 = 67y

y = 4

Veg burger in A = 18 × 4 = 72

Non- veg burger in A = 14 × 4 = 56

Veg burger in B = 15 × 4 =60

Non- veg burger in B = 20 × 4 = 80

Explanation for 16 Question:

Required ratio

= 72: 63

= 8: 7

∴ The ratio of veg burger sold by A and C = 8 : 7

#### 17. Question

Find the sum of non–veg burgers sold by all the shopkeepers.

a) 178

b) 145

c) 156

d) 175

e) 181

Solution:-

Required sum = 56 + 80 + 45 = 181

∴The sum of non veg burger sold by all the shopkeepers is 181.

#### 18. Question

The veg burger sold in B is what percentage of non–veg burgers sold in B?

a) 80%

b) 85%

c) 75%

d) 70%

e) 60%

Solution:

Required % = 60/80 *100 = 75%

Thus, the required percentage is 75%.

#### 19. Question

Find the average veg burger sold in A and B.

a) 44

b) 60

c) 72

d) 66

e) 45

Solution:

Required average = (72 + 60) /2 = 66

∴ The average veg burger sold by A and B is 66.

#### 20. Question

Find the ratio between the burger sold in B to the veg burger sold in C.

a) 1: 2

b) 20: 9

c) 3: 4

d) 9: 20

e) 3: 16

Solution:

Required ratio = (60 + 80): 63 = 20: 9

#### Directions (21-24): Read the following tables carefully and answer the questions that are given below.

A number of contestants ( in lakh ) participating in a fashion designing show from six different cities named P, Q, R, S, T, and U. The successful and unsuccessful contestants ratio of the contestants are given below.

#### 21. Question:

The number of contestants participating in the fashion designing show from city R is what percent of the number of contestants participating in the show from city Q? (Approximate value.)

a) 34%

b) 44%

c) 54%

d) 40%

e) 50%

Sol.

Required percentage

=(1.08 × 100) / 3.14 %

= 34%

Thus the percentage is 34%.

#### 22. Question

What is the respective ratio of the numbers of contestants unsuccessful in the show from city S to those unsuccessful in the show from city P?

a) 215 : 50

b) 221 : 75

c) 223 : 50

d) 227 : 50

e) None of these

Solution:

Required ratio

= (3/4 × 2.27) : (3/10 × 1.25)

= 1.7025 : 0.375

= 227 : 50

Thus, the required ratio is 227:50.

#### 23. Question

The number of contestants qualifying the exam from city U is what percent of the total number of contestants participating from all the cities together? (Approximate value.)

a) 12.93%

b) 21.55%

c) 15.39%

d) 19.72%

e) 25.75%

Solution:

Required percentage

= (2.73 × 7/12) / (1.25 + 3.14 + 1.08 + 2.27 + 1.85 + 2.73) ×100 %

=(1.5925/12.32)× 100%

= 12.93 %

Thus, the required percentage is 12.93%.

#### 24. Question

What is the number of unsuccessful contestants in city S?

a) 1.10 lakh

b) 1.5270 lakh

c) 1.7025 lakh

d) 1.9935 lakh

e) 3.99 lakh

Solution:

Number of unsuccessful contestants in city S

= (2.27 × 3/4) lakh

= 1.7025 lakh

∴ The number of unsuccessful contestants in city S = 1.7025 lakh

#### 25. Question

A trader invests a sum of money in a scheme that offers 4% interest per annum with an increase of 0.5% per annum each year. If he received Rs. 9880 as interest at the end of 4 years, then find the money invested by the trader.

a) 42000

b) 45000

c) 47000

d) 48000

e) 52000

Solution:

(4% + 4.5% + 5% + 5.5%) = 19%

19% = 9880

100% = (9880 × 100) /19

= 52000

∴ Money invested by the trader = 52000

#### 26. Question:

Price of a packet of biscuits Rs. 750 is offered at an 8% discount and the price of a packet of chocolate Rs. 1250 is offered at a 20% discount. If a man buys 5 packets of biscuits and 3 packets of chocolate, then what percentage effective discount does the man get?

a) 14%

b) 17%

c) 18%

d) 20%

e) 25%

Solution:

Total price of 5 packet biscuit and 3 packet chocolate

= (750 × 5) +(1250 × 3)

=7500

Discount in 5 packet Biscuit

= (750 × 5) × 8%

=300

Discount in 3 packet chocolate

= (1250 × 3) × 20%

=750

Total discount

= ( 300 + 750)

= 1050

Required Discount%

= (1050 ×100) /7500

=14%

∴ The man get the effective discount is 14%.

#### 27. Question:

A vessel is full of 80 litres of fruit juice. 1/10 of total fruit juice is taken out and replaced by water. Again, the same amount of mixture was taken out and replaced by water. Find the amount of fruit juice in the final mixture so formed.

a) 50.50 litre

b) 56.20 litre

c) 60.50 litre

d) 64.80 litre

e) 70.50 litre

Solution:

1/10 × 80 = 8 litre

Required fruit juice

= (80 × 81) /100

= 64.8 litre

∴ The amount of fruit juice in the final mixture is 64.8 litres.

#### 28. Question

A train crosses a platform of length 400 meters in 15 sec and the same train crosses a pole in 10 sec. Find the time taken by the same train to cross a bridge of length 200 meters?

a) 12 sec

b) 12.50 sec

c) 15.50 sec

d) 22 sec

e) None of these

Solution:

Let, the length of the train is L meters

Speed = Distance/Time

(L + 400)/15 = L/10

15 L = 10 L + 4000

5 L = 4000

L = 800 meter

The time taken by the train to cross a bridge

Time = Distance/Speed

Required time

= (800 + 200)/(800/10)

= 1000/80

= 12.50 sec

Thus, the time taken by the train = 12.50 sec

#### 29. Question

Amal and Bimal started a business in partnership. Amal invests certain money for one year and after 6 months, Bimal invests Rs. 4000 more than the investment of Amal. The ratio of annual total profit and Amal’s profit is 7:3. Find the investment of Amal.

a) 1200

b) 1400

c) 3600

d) 2400

e) 4800

Solution:

Let, Amal invest Rs. P

Therefore, Bimal invest Rs. = P + 4000

Hence, the ratio of Amal : Bimal’s investment is

= 12 × P : 6 ×(P + 4000)

= 2P : (P + 4000)

Now, according to question, the ration of annual total investment and Amal’s investment,

2P/(3P + 4000) = 3/7

14P = 9P + 12000

5P = 12000

P = 2400

Therefore, the investment of Amal is Rs. 2400.

#### 30. Question

Kapil and Vimal started work and will get money according to their efficiency. A certain amount is the wages for 28 days of Kapil’s work and it is equal to the wages of Vipul’s 21 days of work. That same amount is sufficient to pay the wages of both for how many days?

a) 12 days

b) 15 days

c) 6 days

d) 10 days

e) 8 days

Sol.

Let, the total work (LCM of 28 and 21) is = 84 unit

Within 1 day, Kapil can do = 84/28 = 3 unit

Within 1 day, Vipul can do = 84/21 = 4 unit

Within 1 day, both can work = (3 + 4)  = 7 unit

Together, they can work in = 84/7 = 12 days.

Thus, the same amount of money is sufficient to pay for both in 12 days.

#### There were four different banks named A, B, C, and D. These four banks opened a certain number of accounts in three years 2016, 2017, and 2018. The following graph shows the account opening in four different banks A, B, C, D over the year. #### 31. Question

The percentage increase in account opening by bank B from 2016 to 2017 is about

a) 30.8 %

b) 22.2 %

c) 18.2 %

d) 18.4 %

e) None of these

Sol.

Percentage increase

= {(55 – 45 )/45 } ×100

= 22.2 %

#### 32. Question

Account opening by bank B in 2017 and by bank D in 2018 together is what percent of account opening by bank A in 2016?

a) 50 %

b) 200 %

c) 150 %

d) 75 %

e) None of these

Solution:

Account opening by bank B in 2017 and by bank D in 2018 together

= (55+65) = 120

Account opening by bank A in 2016 = 60

Required percentage

=(120 / 60 ) × 100 %

= 200 %

#### 33. Question

Which one of the four banks has recorded the maximum percentage increase in account opening from 2017 to 2018?

a) A

b) B

c) C

d) D

e) None of these

Solution:

Bank A ={(75 – 70) / 70} × 100 %

=7.14 %

Bank B = negative

Bank C = negative

Bank D = {( 65 – 60 ) / 60} × 100 %

= 8.33 %

So, Maximum percentage increase in bank D.

#### 34.Question

Which bank has recorded the maximum percentage increase in account opening from 2016 to 2017?

a) A

b) B

c) C

d) D

e) None of these

Solution:

Bank A = {( 70 – 60 ) / 60} × 100%

= 16.66 %

Bank B = {( 55 – 45 ) / 45 } × 100 %

= 22.2 %

Bank C = {( 85 – 65 ) / 65 } × 100 %

= 30.77 %

Bank D = {( 60 – 50 ) / 50 } × 100 %

= 20 %

So, the maximum percentage increase in bank C.

#### 35. Question

Find the ratio between the average account opening by four banks in 2017 and average account opening by four banks in 2016 is

a) 25:22

b) 51:50

c) 11:15

d) 27:22

e) None of these

Solution:

In 2017 = ( 70 + 55 + 85 + 60 ) / 4

= 270/4

In 2016 = ( 60 + 45 + 65 + 50) / 4

= 55

Required ratio = 270/4 : 55 = 27:22

Thus, the ratio between the average account opening by four banks in 2017 and the average account opening by four banks in 2016 is 27:22.

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