Sunday, 5 June 2011

SBI-PO 2006 (QUANTITATIVE APTITUDE)

Directions (126-130) ; Each of the questions below consists of a question and three statements denoted A, B and C are given below it. You have to study the questions and all the three statement and decide the question can be answered with anyone or two of the statements or all the statements are required to answer the question.

126. How much marks did Arun secure in English?
A. The average marks obtained by Arun in four subjects including English is 60.
B.The total marks obtained by him in English and Mathematics together is 170.
C. The total marki obtained by him in Mathematics and Science together is 180.
(a) All three A, B and C together are necessary.
(b) Only A and B together are necessary.
(c) Only B and C together are necessary.
(d) Only A and C together are necessary.
(d) None of these
Ans.A. Total marks in 4 subjects including English
= 4 × 60 = 240
B. Total marks in English and Maths = 170
C. Total marks in Maths and Science : 180
The question can't be answered because nothing has been said about the marks in the fourth subject.
Also, there are four unknowns but only three equations can be formed with given data.

Directions ( 131-135) : Study the following table carefully and answer the questions given below it.

127. How much profit did Mahesh earn on the cost price of an article by selling it?
A He got 15% discount on the marked price at the time of purchase.
B. He sold it for Rs. 3060.
C. He earned 2% profit on the marked price.
(a) Only A and B both together are necessary.
(b) Only B and C both together are necessary.
(c) Only A or C and B together are necessary.
(d) Even A,B and C altogether are not sufficient to answer the question.
(e) All three A, B and C together are necessary.
Ans. Let the marked price be Rs. x
A. cost price = (1 -0.15) x = Rs. 0.85x
B. S.P. = Rs. 3060
C. Profit = 2% of x = 0.02x
Profit earned on the cost price

0.02x

0.85x

× 100 ≈ 2.35%

0.02x = 3060 - 0.85x
0.87x = 3060

x =	3060 8.87

Actual profit = 0.02x

= 0.02 ×

3060

0.87

= Rs 70.34

128. What will be sum of two numbers?
A. Among the two numbers, the bigger number is greater than the smaller number by 6.
B. 40% of the smaller number is equal to 30yo of the bigger number.
C. The ratio between half of the bigger number and (1/3)rd of the smaller number is 2 : 1
(a) Only B and C to gather are necessary
(b) Only A and B together are necessary
(c) Out of A, B and C any two together are necessary
(d) All three A, B and C together are necessary
(e) None of these
Ans. A. x - y = 6
B. 0.4y = 0.3x

= 2 : 1

B and C give the same expression/information and hence are equivalent.

x =

x - y = 6
(4/3)y - y = 6
y /3 = 6
y = 18
x = (4/3) × 18 = 24

129. What is the area of a right angled triangle?
A. The perimeter of the triangle is 30 cm.
B. The ratio between the basic and the height ofthe triangle is 5: 12
C. The area ofthe triangle is equal to the area of rectangle of length 10 cms.
(a) Only B and C together are required
(b) Only e and B together are required
(c) Only either A or B and C together are required
(d) Only A and C together are required
(e) None of these
Ans . Hypotenuse = √5² + 12²
= √25 + 144 = √169 = 13
Base : Height : Hypotenuse = 5 : 12 : 13
Base + Height + Hypotenuse = 30 cm

∴ Base =

5 + 12 + 13

× 30 = 5 cm

Height =

5 + 12 + 13

× 30 = 12cm

Area = (1/2) × base × height
= (1/2) × 5 × 12 = 30cm²

130. What is R's share of profit in a joint venture?
A. Q started business investing Rs' 80,000
B. Rejoined him after 3 months.
C P joined after 4 months with a capital of Rs' 1,'20,000 and got Rs. 6,000 as his share of Profit.
(a) Only A and C are required
(b) Only B and C are required
(c) All A, B and C together are required
(d) Pen with all A, B and C the answer cannot be arrived at
(e) None of these
Ans. The question cannot be answered because R's share in investment is not give.

The number of candidates appeared, passed and selected in competitive examination from five states over the years.

State → Year ↓

2000

850

215

1050

245

990

195

1080

300

1120

204

2001

880

240

980

230

650

150

1150

320

960

180

2002

750

180

1120

210

840

180

995

280

885

177

2003

920

290

890

190

780

160

975

260

1040

220

2004

960

300

950

225

1020

220

888

240

980

280

2005

820

250

1180

200

930

215

864

216

900

228

A = Appeared, P = Passed, S = Selected

131. In the year 2000, which state had the lowest percentage of candidates selected over the candidates appeared ?
(a) A
(b) B
(c) C
(d) D
(e) E
Ans. Percentage of candidates selected over appeared in 2000.

A =

850

× 100 = 2.94 %

B =

10 50

× 100 = 3.33 %

C =

99 0

× 100 = 2.83 %

D =

1080

× 100 = 3.33 %

E =

1120

× 100 = 3.57 %

The percentage is lowest for state C.

132. During which of the following years the passing percentage over appeared is the highest from state 'D'?
(a) 2005
(b) 2004
(c) 2003
(d) 2002
(e) None of these
Ans. Passing percentage over appeared for state D in :

2000 →

300

1080

× 100 = 27.7 %

2001→

320

1150

× 100 = 27.8 %

2002→

280

995

× 100 = 28.1 %

2003→

260

975

× 100 = 26.67 %

2004→

240

888

× 100 = 27 %

2005→

216

864

× 100 = 25 %

The required percentage is highest in the year 2002.

133. Total number of candidates selected from state 'A' is approximately what percentage of the total number of candidates selected from state 'B'?
(a) 72
(b) 88
(c) 85
(d) 75
(e) 80
Ans. Total no. of candidates selected from state 'A'
= 25 + 20 + 22 + 36 + 32 + 28
= 163

∴ Required % =

163

203

× 100

≈ 80% (approximate)

134. During which of the following years the percentage of candidates selected over passed is the lowest for state 'B' ?
(a) 2000
(b) 2001
(c) 2003
(d) 2004
(e) None of these
Ans. Percentage of candidates selected over passed for state 'B' in

2000 =

245

× 100 = 14.3%

2001 =

230

× 100 = 13%

2002 =

210

× 100 = 13.3 %

2003 =

190

× 100 = 16.8%

2004 =

225

× 100 = 17.8%

2005 =

200

× 100 = 19%

Required percentage is lowest in 2001.

135. What is the ratio between number of candidates passed from state A in 2001 to that from state E in 2004?
(a) 6 : 7
(b) 14 : 15
(c) 13 : 16
(d) 12 : 16
(e) None of these
Ans. No. of candidates passed from state A in 1996 = 240
No. of candidates passed from state E in 1999 = 280
∴ Required ratio = 240 : 280
= 6 : 7

Directions (136-140) : Study the following graph carefully to answer the question given below it.
Production of paper by 3 different companies A, B & C over the year

136. What is the difference between production of company C in 1991 and the production of company A in 2004 ?
(a) 50, 000 tonnes
(b) 5,00,00000 tonnes
(c) 50,00,000 tonnes
(d) 5,00,000 tonnes
(e) None of these
Ans. Production of company C in 1999 = 45 lakh tonnes.
Production of company A in 2004 = 50 lakh tonnes
∴ Required difference = 50 - 45 = 5 lakh tonnes

137. What is the percentage increase in production 'A' from 2000 to 2001 ?
(a) 37.5
(b) 38.25
(c) 35
(d) 36
(e) None of these
Ans. Required percentage

55 - 40

× 100 =

= 37.5 %

138. For which ofthe following years the percentage of rise/fall in production from the previous year is the maximum for company B?
(a) 2000
(b) 2001
(c) 2002
(d) 2003
(e) 2004
Ans. (b)

139. The total production of company 'C in 2001 and 2004 is what percentage of the total production of company A in 1999 and 2000 ?
(a) 95
(b) 90
(c) 110
(d) 115
(e) 133.33
Ans.(b) Total production of company C in 2001 and 2002 = 120 lakh tonnes
Total production of company A in 1999 and 2000
= 90 lakh tonnes
∴ Required percentage

120

× 100 = 133

140. What is the difference between the average production per year of the company with highest average production and the company with lowest average production in lakh tonnes ?
(a) 3.17
(b) 4.33
(c) 4.17
(d) 3.33
(e) None of these

Directions (140-145) : Study the following graph carefully and answer the questions given below it.
The number of students who joined and left the school in the beginning of year for six years, from 2000 to 2005.
Initial strength of the school in 1999 = 1500

-0- Number of student left -x- Number of students joined
(c) Ans. Average production of company A

=	50 + 40 + 55 + 45 + 60 + 50 6

300

= 50 lakh tonnes

Average production of company B

=	55 + 60 + 50 + 55 + 50 + 55 6

325

= 54.17 lakh tonnes

Average production of company

=	45 + 50 + 60 + 65 + 45 + 40 6

300

= 50 lakh tonnes
∴ Required difference
= 54.17 - 50
= 4.17 lakh tonnes.

141. What was the increase/decrease in strength of the school from 2001 to 2002 ?
(a) Increase by 100
(b) Decrease by 100
(c) Increase by 200
(d) Decrease by 200
(e) None of these
Ans.(a) No of student who left in the beginning of 2002 = 400
No. of students who joined in the beginning of 2002 = 500
∴ There was net increase of 100 (= 500 - 400) students in the strength of the school from 2001 to 2002.

142. For which of the following years, the percentage rise/fall in number of students Left from the previous years is the highest?
(a) 2001
(b) 2002
(c) 2003
(d) 2004
(e) 2005
Ans.(a) We can come to this conclusion even without performing complete exact calculation, simply by looking comparing the terms written within the brackets.

143. How many students were there in the school during the year 2003 ?
(a) 1495
(b) 1600
(c) 1550
(d) 1700
(e) None of these
Ans.(d) Total no. of students who joined till 2003
= 300 + 250 + 500 + 450 = 1500
Total no. of students who left till
2003 = 250 + 350 + 400 + 300 = 1300
Net increase in the strength of the school
= 1500 - 1300 = 200
Initial strength of the school in 1999 = 1500
∴ Strength of the school during 2003 = 1500 + 200 = 1700

144. During which of the following pairs of years, the strength of school is equal ?
(a) 200 and 2002
(b) 2002 and ,2004
(c) 2003 and 2005
(d) 2002 and 2005
(e) 2000 and 2002
Ans. (e)

Year	Strength
1999	1500
2000	1500 + 300 - 250 = 1550
2001	1550 + 250 - 350 = 1450
2002	1450 + 500 - 400 = 1550
2003	1550 + 450 - 300 = 1700
2004	1700 + 400 - 500 = 1600
2005	1600 + 550 - 500 = 1650

Strength of the school was equal in 2000 and 2002.

145. The number of students in 2003 is approximately what percent of the number of student in' 2001 ?
(a) 85
(b) 117
(c) 95
(d) 103
(e) 108
Ans.(b) From solution to Q. No. 159 we have the no. of students in 2003-1700 and that in 2001 = 1450

∴ Required % =

1700

1450

× 100

= 117 % (approx.)

Directions (146-150) In each of the following questions a number series is given. After the series, a number is given followed by (a),(b) (c), (d) and (e) you have to complete the series starting with the number given following the question of the given series. Then answer the question given below it.

146. 9 19.5 41 84.5
12 (a) (b) (c) (d) (e)
Which of the following numbers will come in place of (c) ?
(a) 111.5
(b) 118.5
(c) 108.25
(d) 106.75
(e) None
Ans.(e) The given reries is based on the following pattern:
9 × 2 + 1.5 = 19.5
19.5 × 2 + 2 = 41
41 × 2 + 2.5 = 84.5
Therefore, the new series is as follows :
12 × 2 + 1.5 = 25.4 ................. (a)
25.5 × 2 + 2 = 53 ..................... (b)

53 × 2 + 2.5 =

108.5

............(c)

108.5 × 2 + 3 = 220 ................ (d)
220 × 2 + 3.5 = 443.5 .............(e)
Therefore, the number 108.5 will come in place of (C) in the new series.

147.    4    5   22    201
        7   (a) (b) (c) (d) (e)
Which of the following number will come in place of (d)?
(a) 4948
(b) 4840
(c) 4048
(d) 4984
(e) None of these
Ans.(a) The series is based on following pattern :
4 × 1 + 1 = 5        ↓ + 3 5 × 4 + 2 = 22       ↓ + 5 22 × 9 + 3 = 201
Similarly the new series is as follows :
7 × 1 + 1 = 8 ................. (a)
8 × 4 + 2 = 34 ................ (b)
34 × 9 + = 309 ............... (c)

309 × 16 + 4

4948

............ (d)

Therefore, the number 4948 will come in place of (d) in the new series.

148. 5    5.25      11.5     36.75
       7 (a) (b) (c) (d) (e)
which of the following number will come in place of (c) ?
(a) 34.75
(b) 24.75
(c) 24.5
(d) 34.5
(e) None of these
Ans(b). The series is based on following pattern :
     5 × 1 + 0.25 × 1 = 5.25                              ↓ + 5 5.25 × 2 + 0.25 × 4 = 11.5                              ↓ + 5 11.5 × 3 + 0.25 × 9 = 36.75
Similarly, the new series is as follows.
3 × 1 + 0.25 × 1 = 3.25 ............. (a)
3.25 × 2 + 0.25 × 4 = 7.5 ............. (b)

7.5 × 3 + 0.25 × 9 =

24.75 ............(c)

Therefore, the number 24.75 will come in place of (c) in the new series.

149. 38 19 28.5 71.25
18 (a) (b) (c) (d) (e)
which of the following number will come in place of (d) ?
(a) 118.75
(b) 118.25
(c) 108.25
(d) 118.125
(e) None of these
Ans.(d) The series is based on following pattern :
38 × 0.5 = 19
19 × 1.5 = 28.5
28.5 × 2.5 = 71.25
Similarly, the new series is as follows :
18 × 0.5 = 9 ........... (a)
9 × 1.5 = 13.5 ...........(b)
13.5 × 2.5 = 33.75 ........... (c)

33.75 × 3.5 =

118.125 ...........(d)

Therefore, the number 118.125 will come in place of (d) in the new series.

150. 25 146 65 114
39 (a) (b) (c) (d) (e)
which of the following number will come in place of (e) ?
(a) 122
(b) 119
(c) 112
(d) 94
(e) None of these
Ans.(c) The series is based on following pattern :
25 + (11)² ⇒ 25 + 121 = 146
146 - (9)² ⇒ 146 - 81 = 65
65 + (7)² ⇒ 65 + 49 = 114
Similarly, the new series is as follows :
39 + (11)² ⇒ 39 + 121 = 190 ............ (a)
160 - (9)² ⇒ 160 - 81 = 79 ............. (b)
79 + (7)² ⇒ 79 + 49 = 128 ............. (c)
128 + (5)² ⇒ 128 - 25 = 203 .......... (d)

103 + (3)² ⇒ 103 + 9 =

112

......... (e)

Therefore, the number 112 will come in place of (e) in new series.

Directions (151-155) Read the following statement carefully to answer the given questions.
A committee of 12 persons is to be formed from 9 women and 8 men.

151. In how many ways this can be done if atleast 5 women have to be included in a committee ?
(a) 6000
(b) 6010
(c) 6062
(d) 6005
(e) None of these
Ans.(c) There are 9 women and men. A committee of 12, consisting of at least 5 women, can be formed by choosing :
(i) 5 women and 7 men
(ii) 6women and 6 men
(iii) 7 women and 5 men
(iv) 8 women and 4 men
(v) 9 women and 3 men
∴ Total number of ways of forming the committee
= ⁹C₅ × ⁸C₇ × ⁹C₆ × ⁸C₆ × ⁹C₇ × ⁸C₅ × ⁹C₈ × ⁸C₄ × ⁹C₉ × ⁸C₃
= 126 × 8 + 84 × 28 + 36 × 56 + 9 × 70 + 1 × 56 = 6062

152. In how many of these committees the women are in majority ?
(a) 2000
(b) 2700
(c) 2705
(d) 2702
(e) None of these
Ans.(d) Women are in majority in (iii), (iv) and (v) cases as discussed in question 37 .
∴ Total number of such committees
= ⁹C₇ × ⁸C₅ × ⁹C₈ × ⁸C₄ × ⁹C₉ × ⁸C₃
= 36 × 56 + 9 × 70 + 1 × 56 = 2702

153. In how many of these committees, the men are in majority?
(a) 1008
(b) 1100
(c) 1200
(d) 1225
(e) None of these
Ans.(a) Men are in majority in only (i) case as discussed in question 37.
∴ Total number of such committees
= ⁹C₅ × ⁸C₇ = 126 × 8 = 1008

154. An urn contains 9 red, 7 white and 4 black balls. If two balls are drawn at random, find the probability that both the balls are red.
(a) 17/95
(b) 18/95
(c) 1/12
(d) 91/190
(e) None of these
Ans.(b) There are 20 balls in the urn out of which 2 balls can be drawn in ²⁰C₂ ways.
∴ Total number of elementary events = ²⁰C₂ = 190
There are 9 red balls out of which 2 balls can be drawn in ⁹C₂ ways.
∴ Favorable number of elementary events

= ⁹C₂

9 × 8

1 × 2

= 36

∴ Required probability

190

155. How many different words can be formed with the letters of the word 'ALLAHABAD'?
(a) 7500
(b) 7560
(c) 7510
(d) 7580
(e) None of these
Ans.(b) There are 9 letters in the word ALLAHABAD out of which 4 are A's, 2 are Ls and the rest are all distinct.
So, the requisite number of words

4!2!

= 7560

Directions (156-160) Study the following graph carefully and answer the questions given below :

Total no, of employees 42,980

Total no, of employees 48,640

156. In 2005 the total no. of which of the following types of pairs of employees was approximately equal to A type of employees in 2006?
(a) B and C
(b) A and C
(c) D and E
(d) C and D
(e) C and F
Ans.(d) No. of A type of employees in 2006., = 0.22 × 48640 = 10700
In 2005,
A = 0.20 × 42980 = 8596
B = 0.06 × 42980 = 2579
C = 0.10 × 42980 = 4298
D = 0.15 × 42980 = 6447
E = 0.27 × 42980 = 11605
F = 0.27 × 42980 = 9455
C + D = 4298 + 6447 = 10745

157. From 2005 to 2006 in the case of which of the following types of employees the change was maximum ?
(a) B
(b) D
(c) C
(d) A
(e) None of these
Ans.(a) In 2006,
A : 10700
B : 0.10 × 48640 = 4864
C : 0.11 × 48640 = 5350
D : 0.09 × 48640 = 4377
E : 0.27 × 48640 = 13133
F : 0.21 × 48640 = 10214
% change during 2005 - 2006

A :

10700 - 8596

8596

× 100 ≈ 24.5%

B :

4864 - 2579

2 579

× 100 ≈ 88.6%

5350 - 4298

4298

× 100 ≈ 24.5%

D :

6447 - 4377

6447

× 100 ≈ 32.1%

E :

13133 - 11605

11605

× 100 ≈ 13.2%

F :

10214 - 9455

9455

× 100 ≈ 8 %

The % change was maximum for B.

158. What was the approximate different in the number of B type of employees during 2005 and 2006?
(a) 2285
(b) 2325
(c) 2085
(d) 2620
(e) 1825
Ans.(a) 4864 - 2579 = 2285

159. If the D type of employees in 2006 was 5000, what would have been its approximate percentage in the company ?
(a) 8
(b) 12
(c) 14
(d) 16
(e) 10

Ans.(e)

5000

48640

× 100 = 10.3 % ≈ 10%

160. The no of A type of employees in 2006 was approximately what per cent of the no. of A type of employees in 2005?
(a) 115
(b) 140
(c) 125
(d) 130
(e) 95

Ans(c) .

10700

8596

× 100 ≈ 125%

161. 12 men take 36 days to do a work while 12 women complete (3/4)th of the same work in 36 days. In how days 10 men and 8 women together will complete the same work ?
(a) 6
(b) 27
(c) 12
(d) Data inadequate
(e) None of these
Ans.(b) In 36 days 12 men can do 1 complete work.
In 36 days 12 women can do (3/4)th of the work
Since time and the no. of persons is the same is both cases,
I woman's daily work = (3/4)th of 1 man's daily work 8 women's daily work
= (3/4) × 8 = 6 men's daily work
(10 men + 8 women's daily work)
= (10 men + 6 men)
= 16 men's daily work.
12 men can do the work is 36 days
∴ 16 men can do the work is

36 ×

= 27 days

162. Rs. 800 becomes Rs. 956 in 3 years at certain simple rate of interest. If the rate of interest in increased by 4% what amount will Rs. 800 become in 3 years ?
(a) Rs. 1020.8
(b) Rs. 1025
(c) 1052
(d) Data inadequate
(e) None of these
Ans(c). Increase is interest in 3 years due to increase in rate by 4%

800 × 3 × 4

100

= Rs. 96

Total amount at the end of 3 years
= Rs. 956 + Rs. 96
= Rs. 1052

163. What least number would be subtracted from 427398 so that the remaining number is divisible by 15 ?
(a) 6
(b) 3
(c) 16
(d) 11
(e) None of these
Ans.(b) 427398 = 15 x 28493 + 3
∴ The least number which should be subtracted from 427398 so that it becomes divisible by 15 = 3.

164. A car covers its journey at the speed of 80 km/hour in 10 hours. If the same distance is to be covered in 4 hours, by how much the speed of car will have to increases?
(a) 8km/hr
(b) 10km/hr
(c) 12km/hr
(d) 16km/hr
(e) None of these
Ans.(e) Initial speed = 80 km/hr
Total distance = 80 × 10 = 800 km.

New speed =

800

= 200 km/hr.

Increase in speed
= 200 - 80 = 120 km/hr.

165. What approximate value will come in place of the question mark (?) in the following equation ?
33(1/3)% of 768.9 + 25% of 161.2 - 58.12 = ?
(a) 230
(b) 225
(c) 235
(d) 220
(e) 240
Ans.(e) 33(1/3)% of 768.9 + 25% of 161.2 - 58.12

100

3 × 100

× 768.9 +

100

× 161.2 - 58.12

= 256.3 + 40.3 - 58.12
= 238.48 = 240 (approx.)

166. If on selling 12 notebooks any seller makes a profit equal to the selling price of 4 notebooks, what is his per cent profit ?
(a) 50
(b) 25
(c) 16(2/3)
(d) Data inadequate
(e) None of these
Ans.(a) Profit = Selling price of 4 notebooks cost price = selling price of (12 - 8) = 4 notebooks.

∴ % profit =

× 100 = 50

167. Present age of Rahul is 5 years less than Ritu's present age. If 3 years ago Ritu's age was x, which of the following represents Rahul's present age?
(a) x + 3
(b) x - 2
(c) x - 3 + 8
(d) x + 3 + 8
(e) None of these
Ans.(b) 3 years ago Ritu's age = x
∴ Ritu's present age = x + 3
Rahul's present age = Ritu's present age - 5
= x + 3 - 5 = x - 2

168. A grocer purchased 2 kg. office at the rate of Rs. l5 per kg. and 3 kg. of rice at the rate of Rs. l3 per kg. At what price per kg. should he sell the mixture to earn 33(1/3)% profit on the cost price ?
(a) Rs.28.00
(b) Rs.20.00
(c) Rs.18.40
(d) Rs.17.40
(e) None of these
Ans.(c) Mixture : 2 kg of rice at Rs. 15/kg + 3 kg of rice at Rs 13/kg
Total weight = 2 + 3 = 5 kg
Total cost price = (2 × 15) + (3 × 13)
= 30 + 39 = Rs. 69
Cost price per kg of the mixture
= 69/5 = Rs. 13.80
Selling price to get 33(1/3) % profit

100 + 33(1/2)

100

× Rs. 13.80

400

3 × 100

× Rs. n13.80

= (4/3) × Rs. 13.80 = Rs. 18.40

169. A boat takes 6 hours to travel from place M to N downstream and back from N to M upstream. If the speed of the boat in still water is 4 km.,/hr, what is the distance between the two places?
(a) 8kms.
(b) 12kms.
(c) 6kms.
(d) Data inadequate
(e) None of these
Ans (d)Total time = 6 hours.
Speed of the boat in still water = 4 km/hr
Let the distance between M and N be D. and the speed of the stream be x.

[

4 + x

4 - x

]

= 6

[

4 - x + 4 + x

(x + x) ( 4 - x )

]

= 6

[

4² - x²

]

= 6

16 - x²

= 6

D =

(16 - x²) =

(16 - x²)

Since the speed of the stream (x) is not given, the distance D cannot be determined .

170. Mr. Yadav spends 80% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year are Rs. 5370, how much amount per month he would have spent on clothes and transport ?
(a) Rs.4,037
(b) Rs.8,076
(c) Rs.9,691.20
(d) Rs.4,845.60
(e) None of these
Ans.(e) Let Mr. Yadav's annual Salary be x.
Amount spent on consumables = 0.80 x.
Amount spent on clothes and transport = 0.50 (x - 0.80x)
Saving = x - 0.80 x - 0.10x = 0.10x
∴ 0.10 x = Expenditure on clothes and transport = 5370
∴ Monthly expenditure = 5370/12
= Rs. 447.50

Directions (171-175) : In each question below one or two equation (s) is/are provided. On the basis of these you have to find out relation between P and q.
Give answer (a) if P = q
Give answer (b) if P > q
Give answer (c) if P > q
Give answer (d) if P > q and
Give answer (e) if q > P

171. I. p² + 24 = 10p
II. 2 q² + 18 = l2q
Ans(b). I. p² + 24 = 10p
p² - 10p + 24 = 0
p² - 6p - 4p + 24 = 0
p(p - 6) -4 (p - 6) = 0
(p - 6) (p - 4) = 0
p = 4,6
II. 2q² + 18 = 12q
q² + 9 = 6p
q² - 6q + 9 = 0
(q - 3)² = 0
q = 3
Thus, p > q

172. pq + 30 = 6 p + 5q
Ans.(c) pq + 30 = 6p + 5q
6p + 5q - pq = 30

= 1

(

)

= 1

p = 5 and q = 6
∴ q > p

173. I. q² + q = 2
II p² + 7p + 10 = 0
Ans(e). I. q² + q = 2
q² + q - 2 = 0
q² - q + 2q - 2 = 0
q(q - 1) +2 (q - 1) = 0
(q -1) (q + 2) = 0
q = - 2,1
p² + 7p + 10 = 0
p² + 5p + 2p + 10 = 0
II. p(p + 5) + 2 (p + 5) = 0
(p + 5) (p + 2) = 0
p = -5, -2
Thus, q ≥ p

174. I. p² + 16 = 8p
II. 4q² + 64 = 32q
Ans.(a) I. p² + 16 = 8p
p² - 8p + 16 = 0
(p - 4)² = 0
p = 4
II. 4q² + 64 = 32q
q² + 16 = 8q
q² - 8q + 16 = 0
(q - 4)² = 0
q = 4
Thus, p = q

175. I. 2p² + l2p + 16 = 0
III. 2q² + 14q + 24 = 0
Ans.(d) I. 2p² + 12p + 16 = 0
p² + 6p + 8 = 0
p² + 2p + 4p + 8 = 0
p(p + 2) + 4 (p + 2) = 0
(p + 2) (p + 4) = 0
p = - 2, - 4
II. 2q² + 14q + 24 = 0
q² + 7q + 12 = 0
q² + 3q + 4q + 12 = 0
q(q + 3) + 4 (q + 3) = 0
(q + 3) (q + 4) = 0
q = - 3, - 4
Thus, p≥ q

EN

SBI-PO 2006 (QUANTITATIVE APTITUDE)

0.02x

0.85x

× 100 ≈ 2.35%

0.02x = 3060 - 0.85x
0.87x = 3060

x =	3060 8.87

Actual profit = 0.02x

= 0.02 ×

3060

0.87

= Rs 70.34

= 2 : 1

B and C give the same expression/information and hence are equivalent.

x =

∴ Base =

5 + 12 + 13

× 30 = 5 cm

Height =

5 + 12 + 13

× 30 = 12cm

The number of candidates appeared, passed and selected in competitive examination from five states over the years.

State → Year ↓

2000

850

215

1050

245

990

195

1080

300

1120

204

2001

880

240

980

230

650

150

1150

320

960

180

2002

750

180

1120

210

840

180

995

280

885

177

2003

920

290

890

190

780

160

975

260

1040

220

2004

960

300

950

225

1020

220

888

240

980

280

2005

820

250

1180

200

930

215

864

216

900

228

A = Appeared, P = Passed, S = Selected

A =

850

× 100 = 2.94 %

B =

10 50

× 100 = 3.33 %

C =

99 0

× 100 = 2.83 %

D =

1080

× 100 = 3.33 %

E =

1120

× 100 = 3.57 %

2000 →

300

1080

× 100 = 27.7 %

2001→

320

1150

× 100 = 27.8 %

2002→

280

995

× 100 = 28.1 %

2003→

260

975

× 100 = 26.67 %

2004→

240

888

× 100 = 27 %

2005→

216

864

× 100 = 25 %

∴ Required % =

163

203

× 100

2000 =

245

× 100 = 14.3%

2001 =

230

× 100 = 13%

2002 =

210

× 100 = 13.3 %

2003 =

190

× 100 = 16.8%

2004 =

225

× 100 = 17.8%

2005 =

200

× 100 = 19%

55 - 40

× 100 =

= 37.5 %

120

× 100 = 133

-0- Number of student left -x- Number of students joined
(c) Ans. Average production of company A

=	50 + 40 + 55 + 45 + 60 + 50 6

300

= 50 lakh tonnes

Average production of company B

=	55 + 60 + 50 + 55 + 50 + 55 6

325

= 54.17 lakh tonnes

Average production of company

=	45 + 50 + 60 + 65 + 45 + 40 6

300

Year	Strength
1999	1500
2000	1500 + 300 - 250 = 1550
2001	1550 + 250 - 350 = 1450
2002	1450 + 500 - 400 = 1550
2003	1550 + 450 - 300 = 1700
2004	1700 + 400 - 500 = 1600
2005	1600 + 550 - 500 = 1650

∴ Required % =

1700

1450

× 100

53 × 2 + 2.5 =

108.5

............(c)

309 × 16 + 4

4948

............ (d)

7.5 × 3 + 0.25 × 9 =

24.75 ............(c)

33.75 × 3.5 =

118.125 ...........(d)

103 + (3)² ⇒ 103 + 9 =

112

......... (e)

= ⁹C₂

9 × 8

1 × 2

= 36

∴ Required probability

190

4!2!

= 7560

Directions (156-160) Study the following graph carefully and answer the questions given below :

Total no, of employees 42,980

A :

10700 - 8596

8596

× 100 ≈ 24.5%

B :

4864 - 2579

2 579

× 100 ≈ 88.6%

5350 - 4298

4298

× 100 ≈ 24.5%

D :

6447 - 4377

6447

× 100 ≈ 32.1%

E :

13133 - 11605

11605

× 100 ≈ 13.2%

F :

10214 - 9455

9455

× 100 ≈ 8 %

Ans.(e)

5000

48640

× 100 = 10.3 % ≈ 10%

160. The no of A type of employees in 2006 was approximately what per cent of the no. of A type of employees in 2005?
(a) 115
(b) 140
(c) 125
(d) 130
(e) 95

Ans(c) .

10700

8596

× 100 ≈ 125%

36 ×

= 27 days

800 × 3 × 4

100

= Rs. 96

New speed =

800

= 200 km/hr.

100

3 × 100

× 768.9 +

100

× 161.2 - 58.12

∴ % profit =

× 100 = 50

100 + 33(1/2)

100

× Rs. 13.80

400

3 × 100

× Rs. n13.80

[

4 + x

4 - x

]

= 6

[

4 - x + 4 + x

(x + x) ( 4 - x )

]

= 6

[

4² - x²

]

= 6

16 - x²

= 6

D =

(16 - x²) =

(16 - x²)

= 1

(

)

= 1

Bank PO and Clerk Jobs