Arithmetic Aptitude Previous Question Answers PSC, UPSC, SSC, IBPS

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Arithmetic Aptitude Previous Questions from PSC, UPSC and SSC

A bag contains 4 red, 5 yellow or 6 pink balls. Two balls are drawn at random. What is the probability that none of the balls drawn are yellow in colour
Asked : IBPS PO Preliminary 2015
A1/7
B3/7

C2/7
D5/14
E9/14
Explanation:

Total number of balls = 4+5+6 = 15

Total number of events = ¹⁵C₂=15×14/1×2=105

Number of desired events = ¹⁰C₂= 10×9/1×2=45

∴ Required probability = 45/105 = 3/7

Directions (next five questions) : What should come in place of question mark (?) in the following question ?

Applicable only to next question

1599÷39.99+4/5×2449-120.05=?
Asked : IBPS PO Preliminary 2015
A1680
B1940
C1640
D1880

E1780
Explanation:

1599÷39.99+4/5×2449-120.05=?

⇒ 1600÷40+4/5×2450-120=?

⇒ 40+1960-120=?

⇒ 2000-120=?

⇒ ?=1880

1559.95-7.99×24.96-?²=1154
Asked : IBPS PO Preliminary 2015
A14

B24
C32
D18
E8
Explanation:

1559.95-7.99×24.96-?²=1154

⇒ 1560-8×25-?²=1154

⇒ 1560-200-?²=1154

⇒ ?²=1360-1154

⇒ ?²=206

⇒ ?²=14

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.

Applicable only to next question

I. 5x²+8x+3=0

II. 3y²+7y+4=0
Asked : IBPS PO Preliminary 2015
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
Asked : IBPS PO Preliminary 2015
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
Asked : IBPS PO Preliminary 2015
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
Asked : IBPS PO Preliminary 2015
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
Asked : IBPS PO Preliminary 2015
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)
Asked : IBPS PO Preliminary 2015
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

Applicable only to next question

Number of female members in health club A is what percent less than number of male members in health club B ?
Asked : RBI Grade-B Officer November 2015
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 ?
Asked : RBI Grade-B Officer November 2015
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 ?
Asked : RBI Grade-B Officer November 2015
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?
Asked : RBI Grade-B Officer November 2015
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 ?
Asked : RBI Grade-B Officer November 2015
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)
Asked : RBI Grade-B Officer November 2015
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 ?
Asked : RBI Grade-B Officer November 2015
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.)
Asked : RBI Grade-B Officer November 2015
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) : 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

Applicable only to next question

Statements :

A≥B>C≥F : Z<C≤D<E

Conclusions :
1. A>Z
2. F<E
Asked : RBI Grade - B Officer August 2014
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
Asked : RBI Grade - B Officer August 2014
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
Asked : RBI Grade - B Officer August 2014
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
Asked : RBI Grade - B Officer August 2014
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
Asked : RBI Grade - B Officer August 2014
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.

Applicable only to next question

What percent of the total number of girls in the college do not know Hindi ? ( rounded off to nearest integer)
Asked : RBI Grade - B Officer August 2014
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 ?
Asked : RBI Grade - B Officer August 2014
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 ?
Asked : RBI Grade - B Officer August 2014
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 ?
Asked : RBI Grade - B Officer August 2014
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 ?
Asked : RBI Grade - B Officer August 2014
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 ?
Asked : RBI Grade - B Officer August 2014
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

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

Advertisement revenues (in INR Thousand)generated

from printed version (PV) and online version (OV) of

6 magazines during 6 months

Month	Magazine P		Magazine Q		Magazine R		Magazine S		Magazine T		Magazine U
Month	PV	OV	PV	OV	PV	OV	PV	OV	PV	OV	PV	OV
Jan.	169	163	201	145	136	141	209	168	152	209	131	184
Feb.	144	171	157	139	156	149	132	223	186	217	98	190
Mar.	129	148	204	144	152	174	174	164	116	185	118	219
Apr.	163	139	232	139	168	207	148	172	129	156	174	236
May	113	152	128	151	196	209	132	211	187	139	168	111
June	172	141	142	163	178	243	211	177	154	144	151	194

Applicable only to next question

What is the respective ratio between total advertisement revenues generated from online version of all the given magazines together in February and total advertisement revenues generated from printed version of all the given magazine together in May ?
Asked : RBI Grade - B Officer August 2014
A33:28

B39:28
C27:16
D33:20
E27:22
Explanation:

Required ratio = 1089:924 = 33:28

The respective ratio of advertisement revenues generated from printed version by magazine P to advertisement revenues generated from online version by the same magazine in July is same as the respective ratio of advertisement revenues generated from printed version by Magazine Q to advertisement revenues generated from online version by the same magazine in March. If the advertisement revenue generated from online version by Magazine P in July was INR 1,08,000/-, what was the advertisement revenue generated from printed version by the same magazine in July ?
Asked : RBI Grade - B Officer August 2014
AINR 1,87,000/-
BINR 1,53,000/-

CINR 1,36,000/-
DINR 1,70,000/-
EINR 1,19,000/-
Explanation:

Total advertisement revenue generated from printed version = 108000 ×204/144 = 1,53,000/-