SBI Clerk Prelims 2021 Quantitative Aptitude Questions (Day-54)

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Quadratic equation

Directions (01-05): In the following questions, two equations I and II are given. You have to solve both equations and give answer as,

1) I) 3x² + 30x + 63 = 0

II) y²– 4y – 21 = 0

a) x > y

b) x ≥ y

c) x < y

d) x ≤ y

e) x=y or the relation cannot be established.

2) I) x² – 33x + 162=0

II) y²– 30y + 144=0

a) x > y

b) x ≥ y

c) x < y

d) x ≤ y

e) x=y or the relation cannot be established.

3) I) x² + 23x + 130 = 0

II) 2y²+ 32y + 120 = 0

a) x > y

b) x ≥ y

c) x < y

d) x ≤ y

e) x=y or the relation cannot be established.

4) I) x² – 17x + 52=0

II) y²– 7y – 60=0

a) x > y

b) x ≥ y

c) x < y

d) x ≤ y

e) x = y or the relation cannot be established.

5) I) x² + 15x – 184=0

II) y²– 30y + 176=0

a) x > y

b) x ≥ y

c) x < y

d) x ≤ y

e) x = y or the relation cannot be established.

Profit and loss

6) A shopkeeper offers a discount of 10%. If the ratio of the marked price to cost price is 6:5, what is the profit or loss percentage?

A.4% loss

B.6% profit

C.8% profit

D.5% loss

E.None of these

Mensuration

7) The height and radius of the cone is 24 cm and 7 cm respectively and the radius of the cylinder equal to the radius of the cone. What is the ratio of the curved surface area of the cone to total surface area of the cylinder whose height is 18 cm?

A.1:2

B.3:4

C.2:3

D.4:5

E.None of these

Time and work

8) A and B can complete the work in 24 days and 16 days respectively. They started the work together and after 6 days B left the work. In how many days A alone complete the remaining work?

A.6 days

B.7 days

C.8 days

D.9 days

E.None of these

Partnership

9) A and B started the business with the investment in the ratio of 4: 5. A and B invests them amount in 10 months and 6 months respectively. If the total profit of the business is Rs.17500, then what is the profit share of A?

A.Rs.8000

B.Rs.10000

C.Rs.12000

D.Rs.14000

E.None of these

Ages

10) The ratio of the ages of Sam and Ram is 3: 7 and after 9 years the ratio becomes 15: 29. If Shon is 21 years younger than Ram, what is the sum of the ages of Sam and Shon?

A.49 years

B.56 years

C.63 years

D.42 years

E.None of these

Answers :

1) Answer: D

3x² + 30x + 63 = 0

3x² + 21x + 9x + 63 = 0

3x(x + 7) + 9(x + 7) = 0

(3x + 9)(x + 7) = 0

x = -3, -7

y² – 4y – 21 = 0

y² – 7y + 3y – 21 = 0

y(y – 7) + 3(y – 7) = 0

(y – 7)(y + 3) = 0

y = 7, -3

x ≤ y

2) Answer: E

x² – 33x + 162 = 0

x² – 27x – 6x + 162 = 0

x(x – 27) – 6(x – 27) = 0

(x – 6)(x – 27) = 0

x = 6, 27

y² – 30y + 144=0

y² – 24y – 6y + 144=0

y(y  – 24) – 6(y – 24)=0

(y – 6)(y – 24)=0

y = 6, 24

Relationship between x and y cannot be established.

3) Answer: D

x² + 23x + 130=0

x² + 13x + 10x + 130=0

x(x + 13) + 10(x + 13)=0

(x + 10)(x + 13)=0

x = -10, -13

2y² + 32y + 120=0

2y² + 20y + 12y + 120=0

2y(y + 10) + 12(y + 10)=0

(2y + 6)(y + 10)=0

y = -3, -10

x ≤ y

4) Answer: E

x² – 17x + 52=0

x² – 13x – 4x + 52=0

x(x – 13) – 4(x – 13)=0

(x – 4)(x – 13)=0

x = 4, 13

y² – 7y – 60=0

y² – 12y + 5y – 60=0

y(y – 12) + 5(y – 12)=0

(y + 5)(y – 12)=0

y = -5, 12

Relationship between x and y cannot be established.

5) Answer: D

x² + 15x – 184=0

x² + 23x – 8x – 184=0

x(x + 23) – 8(x + 23)=0

(x – 8)(x + 23)=0

x = 8, -23

y² – 30y + 176=0

y² – 22y – 8y + 176=0

y(y – 22) – 8(y – 22)=0

(y – 8)(y – 22)=0

y = 8, 22

x ≤ y

6) Answer: C

CP = x

MP/CP = 6/5

MP = 6/5 * x

SP = 6/5 * x * 90/100 = 27x/25

Profit percentage = ((27x/25) – x) / x * 100

= 8%

7) Answer: A

Slanting height of the cone = √h2 + r2 = √24² + 7²

= 25 cm

CSA of Cone = 22/7 * r * l

TSA of the cylinder = 2 * 22/7 * r * (h + r)

Required ratio = 22/7 * 7 * 25 : 2 * 22/7 * 7 * (18 + 7)

= 1: 2

8) Answer: D

A = 1/24

B = 1/16

LCM of (16, 24) = 48

A complete the work in one day = 2 units

B complete the work in one day = 3 units

They work together in 6 days = 6 * (2 + 3) = 30 units of work completed

Remaining work = 48 – 30 = 18 units

A alone complete the remaining = 18/2 = 9 days

9) Answer: B

Profit ratio of A and B = 4 * 10: 5 * 6

= 4:3

A’s profit share = 4/7 * 17500 = 10000

10) Answer: A

(3x + 9)/(7x + 9) = 15/29

105x + 135 = 87x + 261

18x = 126

x = 7

Sam = 3 * 7 = 21 years

Ram = 7 * 7 = 49 years

Shon = 49 – 21 = 28 years

Sum of Sam and Shon age = 21 + 28 = 49 years