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Arithmetic Aptitude Questions & Answers (Compiled from UPSC, SSC ,PSC ,IBPS previous question papers)

Directions (next five questions) : In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate option.

I. 5x²+8x+3=0

II. 3y²+7y+4=0
Ax ≤ y
Bx ≥ y

CRelationship between x and y cannot be established
Dx < y
Ex > y
Explanation:

I. 5x²+8x+3=0

⇒ 5x²+5x+3x+3=0

⇒ 5x(x+1)+3(x+1)=0

⇒ (x+1)(5x+3)=0

⇒ x=-1,-3/5

II. 3y²+7y+4=0

⇒ 3y²+4y+3y+4=0

⇒ y(3y+4)+1(3y+4)=0

⇒ (3y+4)(y+1)=0

⇒ y=4/3,-1

∴ x ≥ y

I. 3x2-13x+12=0

II. 3y2-13y+14=0
Ax ≤ y
Bx ≥ y
CRelationship between x and y cannot be established

Dx < y
Ex > y
Explanation:

I. 3x²-13x+12=0

⇒ 3x²-9x-4x+12=0

⇒ 3x(x-3)-4(x-4)=0

⇒ (x-3)(3x-4)=0

⇒ x=4/3,3

II. 3y²-13y+14=0

⇒ 3y²-7y-6y+14=0

⇒y(3y-7)-2(3y-7)=0

⇒(3y-7)(y-2)=0

⇒ y=2,7/3

∴ Relationship between x and y cannot be established

I. 2x²+15x+27=0

II. 2y²+7y+6=0
Ax ≤ y
Bx ≥ y
CRelationship between x and y cannot be established
Dx < y

Ex > y
Explanation:

I. 2x²+15x+27=0

⇒ 2x2+9x+6x+27=0

⇒ x(2x+9)3(2x+9)=0

⇒ (x+3)(2x+9)=0

⇒ x=-9/2,-3

II. 2y²+7y+6=0

⇒ 2y2+4y+3y+6=0

⇒ 2y(y+2)+3(y+2)=0

⇒ (y+2) (2y+3) = 0

⇒ y=-2,-3/2

∴ x < y

I. 2x²-9x+10=0

II. 2y²-13y+20=0
Ax ≤ y

Bx ≥ y
CRelationship between x and y cannot be established
Dx < y
Ex > y
Explanation:

I. 2x²-9x+10=0

⇒ 2x²-5x-4x+10=0

⇒ x(2x-5)-2(2x-5)=0

⇒ (2x-5)(x-2)=0

⇒ x=2,5/2

II. 2y²-13y+20=0

⇒ 2x²-8y-5y+20=0

⇒ 2y(y-4)-5(y-4)=0

⇒ (y-4)(2y-5)=0

⇒ y=5/2,4

∴ x ≤ y

I. x²=144;

II. y2-24y+144=0
Ax ≤ y

Bx ≥ y
CRelationship between x and y cannot be established
Dx < y
Ex > y
Explanation:

I. x²=144

⇒ x=√144=± 12

II. y²-24y+144=0

⇒ y²-12y-12y+144=0

⇒ y(y-12)-12(y-12)=0

⇒ (y-12)(y-12)=0

⇒ y=12

∴ x ≤ y

The time taken by a boat to travel a distance downstream is half the time taken by it to travel the same distance upstream. What is the speed of the boat downstream if it travels 7.5 km upstream in 1 hour 30 min ? (in km/h)
A7.5
B5
C9
D10

ENone of these
Explanation:

Time taken by boat upstream = 1 ¹/₂

=3/2 hour

Time taken by boat downstream

= 3/2×1/2=3/4 hour

∴ Speed of boat downstream

=7.5×4/3 = 10 km/h

Directions (Next Five Questions) : Refer to the pie-charts and answer the given questions.

Distribution of total number of members

(both male and female) in 5 health clubs in 2008

Total number = 4200

Distribution of total numbe rof male members in 5 health clubs in 2008

total number = 2400

Number of female members in health club A is what percent less than number of male members in health club B ?
A52%
B64%
C58%
D62%
E54%

Explanation:

Number of female members in health club A = 4200×18/100-2400×20/100

= 756-480 = 276

Number of male members in health club B = 2400×25/100 = 600

∴ Required percentage = 600-276/600 ×100

= 54%

What is the central angle corresponding to number of members (both male and female) in health club B ?
A80.4⁰
B88.8⁰
C86.4⁰

D98.2⁰
E92.6⁰
Explanation:

Required central angle = 24/100 ×360 = 86.4⁰

Only 50% of the members (both male and female0 in health club E have lifetime membership. If the number of females in health club E who have lifetime membership is 44, what percent of male members in health club E have lifetime membership ?
A48 2/3%
B54 1/3%,
C57 1/34%,
D51 2/3%,

E60 1/3%
Explanation:

Total number of members in health club E have lifetime membership = 4200×8/100×50/100 = 168

Number of females in health club E who have lifetime membership = 44

Number of male members in health club E = 2400×10/100 = 240

∴ Percentage of male members in health club E have lifetime membership = 168-44/240 ×100

= 51 2/3%

What is the average number of female members in health clubs C, D and E?
A374
B376
C372

D392
E384
Explanation:

The number of members (both male and female) in health club C = 4200×35/100

= 1470

The number of male members in health club C = 2400×33/100 = 792

The number of female members in health club C = 1470-792 = 678

The number of members (both male and female) in health club D = 4200×15/100 = 630

The number of male members in health club D = 24000×12/100 = 288

The number of female members in health club D = 630-288 = 342

The number of members (both male and female) in health club E = 4200×8/100 = 336

The number of male members in health club E = 24000×10/100 = 240

The number of female members in health club E = 336-240 = 96

∴ Required average = 678+342+96/3

= 1116/3 = 372

What is the central angle corresponding to the number of members (both male and female) in health club A ?
A64.8⁰

B58⁰
C48⁰
D56.4⁰
E62.5⁰
Explanation:

Required central angle = 18×360/100

= 64.8º

A water tank has one inlet, A and one outlet, B. A takes 5 hours to fill the empty tank, when B is not open and B takes 8 hours to empty the full tank, if the tank is three fifth full, how much time will it take to fill the tank completely when both A and B are opened simultaneously ?(in hours)
A6 1/3
B4 1/3
C8 1/3
D5 1/3

E7 1/3
Explanation:

If the tank is 3/5th full, then remaining empty tank will be = 1-3/5 = 2/5th

A and B can fill the empty tank in = 5×8/8-5 = 40/3 hour

Then 2/5th tank fill in = 40/3×2/5 = 5 1/3 hour

In a village, 30% of the villagers belong to upper economic class. The number of villagers who belong to middle economic class are 3/2 of the number of villagers who belong to lower economic class. If 6860 villagers belong to lower economic class, what is the population of the village ?
A22600
B24500

C26000
D25500
E24300
Explanation:

Villagers belong to lower economic class = 6860

Villagers belong to middle economic class = 3/2 ×6860

= 10290

Let the population of village be x.

According to question, 30/100x+10290+6860 = x

17150= x-3/10x

17150×10/7 = x

x = 24500

Boat A travels upstream from point X to point Y in 2 hours more than the time taken by Boat B to travel downstream from point Z to point Y. The distance between X and Y is 40 km and the distance between Y and Z is 24km. The speed of Boat A in still water is equal to the speed of Boat B downstream. What is the speed of Boat A in still water ? (Consider the speed of the current to be the same.)
A20 km/h
B10 km/h
C12 km/h

D14 km/h
E8 km/h
Explanation:

Let the speed of the current = x km/h

Speed of boat B in still water = 10km/h

Speed of boat B in downstream = x+10

Speed boat A in still water = x+10

Speed of boat A in upstream = x+10-x

= 10km/h

According to question,

40/10-24/10+x = 2

4-24/10+x = 2

24/10+x = 2

10+x = 12

x= 2

∴ Speed of boat A in still water = 10+2

= 12km/h

Directions (Next Five Questions) : study the table and answer the given questions.

Data related to human resource of a multinational

company (X) which has 145 offices across 8 countries

Country	Office	Total number of employees	Respective ratio of male and female employees
A	16	2568	5:7	75
B	18	2880	11:5	65
C	14	2310	10:11	40
D	22	3575	3:2	60
E	13	2054	7:6	50
F	17	2788	20:21	75
G	24	3720	8:7	55
H	21	3360	9:5	80

Which of the given countries has the highest number of average employees per office ?
AF
BH
CB
DC

ED
Explanation:

Average employees in country F = 2788/17 = 164

Average employees in country H = 3360/21 = 160

Average employees in country B = 2880/18 = 160

Average employees in country C = 2310/14 = 165

Average employees in country D = 3575/22 = 162.5

What is the difference between the average number of post-graduate employees in countries A,B and D together and the average number of Post-graduate employees in countries F,G and H together ?
A282
B276
C316
D342
E294

Explanation:

The aeverage number of post-graduate employees in countries A,B and D

= 1/3(2568×75/100+2880×65/100+3575×60/100)=1981

The average number of post-graduate employees in countries F, G and H

= 1/3(2788×75/100+3720×55/100+3360×80/100) = 2275

∴ Required difference = 2275-1981 = 294

What is the respective ratio between total number of male employees in countries B and H together and total number of female employees in countries C and D together?
A63:52
B51:38
C77:64
D69:44

E57:40
Explanation:

Total number of male employees in countries B and H = 2880 ×11/16 + 3360 × 9/14 = 4140

Total number of female employees in countries C and D = 2310 ×11/21 +3575 ×2/5 = 2640

∴ Required ratio = 4140: 2640 = 69:44

In which of the given countries is the percentage of women employees to the number of employees (both male and female) in that country the second lowest ?
AG
BB
CE
DH

ED
Explanation:

Female employees in country G = 3720 ×7/15 = 1736

Percentage of women employees in country G = 1736/3720 ×100 = 46.6%

Female employees in country B = 2880 × 5/16 = 900

Percentage of women employees in country B = 900/2880 ×100 = 31.25%

Female employees in country E = 2054 ×6/13 = 948

Percentage of women employees in country E = 948/2054 ×100= 46.15%

Female employees in country H = 3360 ×5/14 = 1200

Percentage of women employees in country H = 1200/3360 ×100 = 35.71%

Female employees in country D = 3575 ×2/5 = 1430

Percentage of women employees in country D = 1430/3575 ×100 =40%

If the number of male Post-graduate employees in Country H is 1800, what per cent of female employees in that particular country is Post-graduate ?
A76%
B74%

C72%
D64%
E68%
Explanation:

Total number of employees = 3360

Ratio of male and Female = 9:5

Number of males = 9/14 ×3360 = 2160

Number of females = 3360-2160 = 1200

Total post-graduate employees = 80/100 ×3360 = 2688

Male post-graduate employees = 1800

∴ Female post post-graduate employees = 2688-1800 = 888

∴ Percentage of female post-graduate employees = 888/1200 × 100=74%

Directions (Next five Questions) : Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data given in the statements are sufficient to answer the questions. Read both the statements

Statements :

A≥B>C≥F : Z<C≤D<E

Conclusions :
1. A>Z
2. F<E
AIf only conclusion I is true.
BIf only conclusion II is true.
CIf either conclusion I or II is true.
DIf neither conclusion I nor II is true.
EIf both conclusion I and II are true.

Explanation:

A≥B>C≥F

E>D≥C>Z

Conclusions :

I. A>Z → True

II. F<E → True

Statements :

P≤O<I; P>Y>W

Conclusions :
1. Y≤I
2. O>W
AIf only conclusion I is true.
BIf only conclusion II is true.

CIf either conclusion I or II is true.
DIf neither conclusion I nor II is true.
EIf both conclusion I and II are true.
Explanation:

I>O≥P>Y>W

Conclusions :

I. Y≤I → False

II. O>W → True

Statements :

D>H≥N; S>I≤H

Conclusions :
1. N ≤S
2. I<D
AIf only conclusion I is true.
BIf only conclusion II is true.

CIf either conclusion I or II is true.
DIf neither conclusion I nor II is true.
EIf both conclusion I and II are true.
Explanation:

D>H≥I<S

I≤H≥N

Conclusions :

I. N≤S → False (Relationship not exist)

II. I<D → True

Statements :

H = I ≤ R; M≥ R < S

Conclusions :
1. M=I
2. M>I
AIf only conclusion I is true.
BIf only conclusion II is true.
CIf either conclusion I or II is true.

DIf neither conclusion I nor II is true.
EIf both conclusion I and II are true.
Explanation:

S>M≥R≥I = H

Conclusions :

I. M=I

II. M>I Either I or II is true

statements :

T<P≤U ; L>U≤K; P≥R

Conclusions :
1. K≥R
2. L>R
AIf only conclusion I is true.
BIf only conclusion II is true.
CIf either conclusion I or II is true.
DIf neither conclusion I nor II is true.
EIf both conclusion I and II are true.

Explanation:

L>K≥U≥P≥R>T

Conclusions : I. K≥R → True

II. L>R → True

Directions (Next Seven Questions) : Study the following information carefully to answer the questions.

In a medical college, there are 1600 students studying Dentistry and Homeopathy. Each student from each course knows one or more languages out of English, Hindi and Bangla. 45% of the students study Dentistry and remaining students study Homeopathy.

Out of the students studying Dentistry boys and girls are in the ratio of 5:3 respectively.

Out of the boys studying Dentistry, 16% know only English, 10%know only Hindi and 4% know only Bangla. 24% know English as well as Hindi, 20% English as well as Bangla, 14% know Hindi as well as Bangla. Remaining boys know all three languages.

Out of the girls studying Dentistry, 20% know only English, 10% know only Hindi and 10% know only Bangla. 20% know English as well as Hindi, 20% know English as well as Bangla, 10% know Hindi as well as Bangla. Remaining girls know all three languages.

Out of the students studying Homeopathy boys and girls are in the ratio of 4:7 respectively.

Out of the boys studying Homeopathy, 20% know only English, 15% know only Hindi and 5% know only Bangla. 15% know English as well as Hindi,25% know English as well as Bangla, 10% know Hindi as well as Bangla. Remaining boys know all three languages.

Out of the girls studying Homeopathy, 15% know only English, 15% know only Hindi and 5%know only Bangla. 20% know English as well as Hindi, 20% know English as well as Bangla, 15% know Hindi as well as Bangla. Remaining girls know all three languages.

What percent of the total number of girls in the college do not know Hindi ? ( rounded off to nearest integer)
A38%
B46%
C48%
D36%
E43%

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Required Percentage = (54+27+54+84+28+112)/(270+560)

= 359/830 × 100

= 43%

Out of the total number of students studying Dentistry, what percent knows at least two languages ?
A61 12/13%
B57 13/16%
C59 13/17%
D66 1/4%

E62 12/19%

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Required Percentage = (108+90+63+54+54+54+27+27)/720 ×100

477/720 ×100

= 66¼%

Out of the students studying Homeopathy, what is the ratio between number of boys knowing English and number of girls knowing Hindi respectively ?
A3:5
B2:3

C9:11
D9:13
E1:3

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Required ratio = 64+48+80+32/84+112+84+56

=224/336 = 2:3

How many students studying Homeopathy, do not know English ?
A292

B232
C228
D298
E207

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Required number of students = 48+84+16+28+32+84 = 292

What percent of the total number of girls in the college know Bangla ?
A45%
B40%
C48%
D42%
E50%

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Total number of girls know Bangla = 27+54+27+27+28+112+84+56

= 415

∴ Required percentage = 415/(270+560) ×100

= 50%

Total how many students in the college know all three languages ?
A108
B132
C169

D137
E142

Explanation:

Student	Dentistry (720)		Homeopathy (880)
Student	Boy (450)	Girl (270)	Boy (320)	Girl (560)
E	72	54	64	84
H	45	27	48	84
B	18	27	16	28
E + H	108	54	48	112
E + B	90	54	80	112
H + B	63	27	32	84
H + E+ B	54	27	32	56

Total students know all three languages = 54+27+32+56 = 169