IPPB Scale-1 Officer Prelims 2017 - Day 16 (Mock Test - 1)

Directions(1-5) : Find the missing numbers in the given series


1. 2, 24, _, 320, 750, 1512

A. 45
B. 54
C. 81
D. 27
E. None of these

Sol. E) None of these.
1³×2 = 2
2³×3 = 24
3³×4 = 108
4³×5 = 320
5³×6 = 750
6³×7 = 1512

2. 2, 7, 17.5, 35.5, _, 102

A. 55.5
B. 63
C. 60.5
D. 50.5
E. None of these

Sol. 2.5*2 + 2 = 7
     3.5*3 + 7 = 17.5
     4.5*4 + 17.5 = 35.5
     5.5*5 + 35.5 = 63
     6.5*6 + 63 = 102.

3. 5, 17, 72, _, 2204, 15438

A. 360
B. 350
C. 321
D. 318
E. None of these

Sol. 5*3 + 2 = 17
    17*4 + 4 = 72
    72*5 + 6 = 366
   366*6 + 8 = 2204

4.  12, 20, _, 57, -68

A. 2
B. 15
C. -7
D. -2
E. None of these

Sol. 12 + 2^3 = 20
     20 - 3^3 = -7
     -7 + 4^3 = 57
     57 - 5^3 = -68

5. 68, 62, _, 54, 84

A. 76
B. 72
C. 74
D. 70
E. None of these

Sol. 68 - (2*3) = 62
     62 + (3*4) = 74
     74 - (4*5) = 54
     54 + (5*6) = 84

6. The average of 11 numbers is 12. The average of first 6 is 11 and that of last 6 is 12, what is the middle number ?

A. 8
B. 6
C. 7
D. 5
E. None of these

Sol. Sum of 11 numbers = 11×12 = 132.
Sum of first 6 numbers = 11×6 = 66.
Sum of last numbers = 12×6 = 72.

Thus the middle number is = (72+66) - 132 = 6.

7. A train is travelling at a speed of 40 kmph. A man is going in the same direction parallel to the train at speed of 25 kmph. If the train crosses the man in 48 seconds, the length of the train is ?

A. 100m
B. 150m
C. 200m
D. 250m
E. None of these

Sol. Relative speed = 40 - 25 = 15 kmph
Length of the train = 15×(48/3600)×1000× = 200m.

8. A rectangular carpet has an area of 100 sq.m and a perimeter of 54 m. The length of its diagonal is ?

A. 23
B. 27
C. 24
D. 25
E. None of these

Sol. Perimeter of a rectangle = 2(l+b)
2(l+b) = 54
l+b = 27
Area of rectangle = l×b
l×b = 100
Diagonal = √l²+b² = √(l+b)² - 2lb = √(27)² - 2×100 = √529 = 23.

9. An amount of Rs 2109 is distributed among A, B and C in the ratio 3:7:9. B's share is more than C's share by ?

A. Rs 444
B. Rs 379
C. Rs 265
D. Rs 215
E. None of these

Sol. Let the shares of A, B & C be 3X, 7X and 9X respectively.
3X + 7X + 9X = 2109
19X = 2109
X = 111.
Difference in the share of B & C = 7X - 3X = 4X = 4×111 = Rs 444.

10. A man rows upstream 17 km and 29 km downstream, taking 5 hours each time. The velocity of the current is  ?

A. 1
B. 1.2
C. 1.4
D. 1.6
E. None of these

Sol. Let speed of boat be 'x' kmph
And speed of current be 'y' kmph
According to the question,
x - y = 17/5
and
x + y = 29/5

Solving, we get, y = 1.2 mph.

11. Prachi sold two steel chairs for Rs 500 each. On one he gains 25% and on other, he loses 20%. How much does she gain or lose in th whole transaction ?

A. 1.5% gain
B. 2% gain
C. 2.4% loss
D. 2% loss
E. None of these

Sol. S.P. of 1st chair = Rs 500
Gain = 25%
Thus, C.P. of 1st chair will be = (500×100)/(100+25) = 400
S.P. of 2nd chair = Rs 500
Loss = 20%
C.P. of 2nd chair = (500×100)/(100-20) = 625.

Total SP = Rs 1000
Total CP = Rs 1025

loss% = (25/1025)×100 = 2.43%.


12. 3 men can do apiece of work in 18 days. 6 boys can also do the same work in 18 days.In how many days, 4 men and 4 boys together will finish the same work ?

A. 12
B. 6
C. 10
D. 8
E. None of these

Sol. According to the question,
3 men = 6 boys
thus, 1 man = 2 boys
4 men + 4 boys = 4 men + 2 men = 6 men
3 men can do work in 18 days
thus, 1 man can do work in 18×3 days
6 men can do the work in (18×3)/6 = 9 days.

13. Six years ago, karan was twice as old as sushma. If the ratio of their present ages is 9:5 respectively, what is the difference between their present ages in years ?

A. 24
B. 30
C. 5
D. 1
E. Cant be determined

Sol. Let the present ages of karan and sushma be x and y..
According to the question,

x/y = 9/5
and
(x-6) = 2(y-6)

Solving, we get, x = 54 & y = 30
Thus, difference = 54-30 = 24 years.

14. An item sold at 10% discount gives 17% profit, what would be the percentage profit if discount increased to 15% ?      

A. 12%
B. 11%
C. 10%
D. 10.5%
E. None of these

Sol. Lets assume C.P. to be 100
Then S.P. will be 117 (as profit 17%)

Now, 117 = (90/100)*M.P.   (As discount is 10%)
     M.P.= 130

When discount 15%, S.P. = (85/100)*130 = 110.5
Thus, profit % = 10.5 %.

15. What is the area of the square whose side is equal to the side of an equilateral triangle with area 9√3?

A. 16
B. 36
C. 18
D. 24
E. None of these

Sol. Lets say the side of the square  = side of the equilateral triangle be 'a'.
Now, area of the triangle is given 9×√3,thus,
[a×a×√3]/4 = 9×√3
a = 6.

16. 15 women can complete 10% of the work in 7 days, 25 women worked for 31.5 days then what fraction of the work is remaining ?

A. 1/5
B. 1/6
C. 1/4
D. 1/3
E. None of these

Sol. 25 women complete the work in = (15×70)/25 = 42 days

25 women per day work = 1/42
25 women 31.5 day work = 31.5/42

Remaining work = (1 - 31.5/42) = 1/4.

17. There are 32 cards in a bag numbered from 1 to 32. 2 cards are drawn one by one without replacement. Find the probability that both are even numbered cards.

A. 1/16
B. 15/62
C. 16/62
D. 15/31
E. None of these

Sol. Required Probability = (16/32)×(15/31) = 15/62.

18. A and B enetered into a partnership with the investments of 25500 and 15000. At the end of 1 year B invested 9000 rs more. The total profit earned at the end of 2 yrs is 45,000 then find the difference between the shares of A and B.

A. 5000 RS
B. 6000 RS
C. 7000 RS
D. 8000 RS
E. None of these

Sol. (25500×2):(15000 + 24000)
= 17:13
Required Difference = (4/30)*45000 = Rs 6000.

19.  Two trains of length 200m each running in the same direction cross each other in 80 sec. If the speed of faster traiin is 72 km/hr, then find the speed of the slower train.

A. 36 km/hr
B. 45 km/hr
C. 54 km/hr
D. 57 km/hr
E. None of these

Sol. Relative speed = 400/9 = 5m/s
     Speed of faster train = 72×(5/18) = 20m/s
     Speed of slower train = 20 - 5 = 15m/s
     or 15×(18/5) = 54 km/h.

20. Out of three numbers, the first is twice the second and is half of the third. If the avg. of 3 numbers is 56, the three numbers in order are:

A. 48,96,24
B. 48,24,96
C. 96,24,48
D. 96,48,24
E. None of these

Sol. Sum of three numbers = 56×3 = 168
     Let 2nd no. = x
     1st no. = 2x
     3rd no. = 4x
 x + 2x + 4x = 168
The no.s are 48,24,96. 

The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.
             Ratio of Value of Imports to Exports by a Company Over the Years.




21.If the imports in 1998 was Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was ?

A. Rs. 250 crores       
B. Rs. 300 crores         
C. Rs. 357 crores       
D. Rs. 420 crores
E. Rs. 450 crores

Sol. D
The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.Let the exports in the year 1998 = Rs. x crores.
Then, the exports in the year 1999 = Rs. (500 - x) crores.
1.25 = 250/x 
x = 250/1.25 = 200        [ Using ratio for 1998 ]
Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.
Let the imports in the year 1999 = Rs. y crores.
Then, 40 = y/300 
y = (300 * 1.40) = 420
Imports in the year 1999 = Rs. 420 crores.

22. The imports were minimum proportionate to the exports of the company in the year ?

A. 1995                     
B. 1996                     
C. 1997                     
D. 2000
E. 1998

Sol. C
The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.

23. What was the percentage increase in imports from 1997 to 1998 ?

A. 72                       
B. 56                         
C. 28               
D. Data Inadequate
E. 30

Sol. D
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.

24. If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was ?

A. Rs. 370 crores     
B. Rs. 320 crores       
C. Rs. 280 crores   
D. Rs. 275 crores
E. Rs. 300 crores

Sol. B
Ratio of imports to exports in the year 1996 = 0.85.
Let the exports in 1996 = Rs. x crores.
Then , 272/x = 0.85 
x = 272/0.85 = 320                   
Exports in 1996 = Rs. 320 crores.

25. In how many of the given years were the exports more than the imports ?

A. 1                       
B. 2                     
C. 3                     
D. 4
E. 5

Sol. The exports are more than the imports imply that the ratio of value of imports to exports is less than 1.
Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.
Thus, there are four such years.


Direction  (26-30): Study the following graph carefully and answer the questions given below it.



26. What is the total number of students studying B.Sc in all the colleges together?

(1) 1825  
(2) 1975
(3) 1650  
(4) 1775
(5) None of these

Sol. (3)
Let the amount of Royalty to be paid for these books be Rs. r.
Then, 20 : 15 = 30600 : r
r = Rs. 22,950

27. What is the respective ratio of total number of students studying B.Sc. in the Colleges C and E together to those studying B.A. in the Colleges A and B together?

(1) 24 : 23  
(2) 25 : 27
(3) 29 : 23  
(4) 29: 27
(5) None of these

Sol. (3)
Central angle corresponding to Royalty = (15% of 360)º
[(15/100) *360] = 54

28. What is the respective ratio of total number of students studying B.Sc., B.A. and B. Com in all the colleges together?

(1) 71 : 67 : 75  
(2) 67 : 71 : 75
(3) 71 : 68 : 75   
(4) 75 : 71 : 68
(5) None of these

Sol. (2)
Clearly, marked price of the book = 120% of C.P.
Also, cost of paper = 25% of C.P
Let the cost of paper for a single book be Rs. n.
Then, 120 : 25 = 180 : n
n =  Rs. 37. 50

29. Number of students studying B.Com. in College C forms approximately what per cent of the total number of student studying B. com in all the Colleges together?

(1) 39%  
(2) 21%
(3) 44%  
(4) 33%
(5) 17%

Sol. (1)
For the publisher to earn a profit of 25%, S.P. = 125% of C.P.
Also Transportation Cost = 10% of C.P
Let the S.P. of 5500 books be Rs. x.
Then, 10 : 125 = 82500 : x.
x = Rs. [(125 x 82500) x 10]= Rs. 1031250
S.P. of one book = Rs. (1031250/ 5500)= Rs. 187.50

30. Number of students studying B. A. in College B forms what per cent of total number of students studying all the disciplines together in that college? ( Rounded off to two digits after decimal)

(1) 26.86  
(2) 27.27
(3) 29.84  
(4) 32.51
(5) None of these

Sol. (4)
Printing Cost of book = 20% of C.P.
Royalty on book = 15% of C.P.
Difference = (20% of C.P.) - (15% of C.P) = 5% of C.P.
Percentage difference = [ (Difference/Printing) * 100%
= [ ( 5% of C.P./Printing Cost ) x 100%]
= 25%.

Directions(31-35) : Simplify the below given equations to find the unknown :

31. (50)3 ÷ (25)2 + 2466 = ?

A. 2666
B. 2654
C. 2456
D. 2342
E. None of these

Sol. (50×50×50)/(25×25) = 200

200+2466 = 2666.

32. (7.84)1/2 × (47.61)1/2 – 92161/2  = ?

A. - 78.68
B. - 78.86
C. - 76.68
D. -78.68
E.  None of these

Sol. = 2.8 ×6.9 – 96

= 19.32 – 96

= – 76.68 

33. 1235 .05÷125 × 32.03 + 0.04 = ?

A. 5642.9
B. 6574.8
C. 374.41
D. 317.14

E. None of these

Sol. 9.9 × 32.03+0.04 = 317.14

34. (15.25) 2 + (0.50)2 – (65.65)2 + (26.67)2 – (18.98)2 = ?

A. -6543
B. -4567
C. -3726
D. -3278

E. None of these

Sol. 232.56+0.25- 4310 + 711.29 – 360.24 = -3726.14

35. (13824)1/3 + (5776)1/2  =x2

A. 20
B. 100
C. 15
D. 10

E. None of these

Sol. 24+76 = 100.

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IBPS PO Prelims Quant MockTest-2 2016-17

1. A, B and C undertake a job for Rs 16000. A can complete the work in 4 days, B can complete the work in 8 days and C can complete the work in 16 days. With the help of a fourth man they complete the work in 2 days. Find fourth man's share ?

A. Rs 1000
B. Rs 2000
C. Rs 500
D. Rs 600
E. None of these

2. Two trains travels towards each other from stations X and Y respectively. The distance between X and Y is 260 km. If its given that the trains meet each other 2 hrs after starting from their respective stations, then find the sum of their speeds ?

A. 160
B. 260
C. 130
D. 75
E. None of these

3. How many kg of sugar at 42 paise/kg must a man mix with 25 kg of 24 paisa/kg so that on selling the mixture at 40 paise/kg he gains 25% profit ?

A. 20 kg
B. 15 kg
C. 10 kg
D. 18 kg
E. 12 kg

4. The average age of a man and his son is 30 years. The ratio of their ages is 7 : 3. What is the difference between the ages of the man and his son?

A. 24
B. 32
C. 16
D. 20
E. None of these

5. A car covers a distance of 960 km in 16 hours. What is the average speed of the train, if the speed of the train is 30% less than the speed of the car?

A. 45
B. 42
C. 50
D. 60
E. None of these

6. A bag contains 6 black balls and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 4/7
B. 3/4
C. 4/5
D. 1/8
E. None of these

7. In simultaneous throw of two coins, the probability of getting at least one head is:

A. 1/2
B. 2/3
C. 3/4
D. 1/3
E. None of these

8. Sohan got 54 marks in Hindi, 65 marks in Science, 89 marks in Maths, 69 marks in Social Science and 68 marks in English. The maximum marks of each subject are 100. How much overall percentage of marks did he get? 

A. 74 
B. 69
C. 68
D. 72
E. None of these

9. Of the adult population in a certain city, 45% of men and 25% of women are married. If no man marries more than one woman, and vice versa, the percentage of total population of adults who are married, is:

A. 31.1%
B. 30%
C. 33.33%
D. 32.14%
E. None of these

10. In a test, A scored 10% more than B and B scored 5% more than C. If C scored 300 marks out of 400, then A’s marks are:

A. 350
B. 360
C. 310
D. 325
E. None of these

Directions(11-15): Study the pie-chart and answer the following questions.
The following pie-charts show the break-up of annual expenditures of two private-sector companies:

11. The amount spent on transport by Pam-Tech is what percentage of the amount spent by Ram-Tech on transport?

A. 30%

B. 35%

C. 40%

D. 45%

E. None of these

12. The expenditure on raw material for both companies taken together, is what fraction of the total expenditure in 2008?

A. 0.2 

B. 0.25

C. 0.3

D. 0.4

E. None of these

13. Both RamTech and PamTech spend the same amount on which category?

A. Rent

B. Transport

C. Salaries

D. Others

E. None of these

14. For which category the difference in expenditure is maximum?

A. Telephone & Electricity Bill

B. Transport

C. Salaries

D. Raw Material

E. None of these

15. The amount spent on salaries by PamTech is what percentage more than the amount spent by RamTech on trent?

A. 50%

B. 65%

C. 60%

D. 45%

E. None of these

Directions(16-20): What should come in place of the question mark in the following series:

16. 13,14,30,93, ?

A. 382
B. 376
C. 366
D. 327
E. 380

17. 9,11,16,33,98,?

A. 326
B. 336
C. 331
D. 340
E. 355

18. 8,14,25,46,82,?

A. 138
B. 153
C. 166
D. 139
E. 135

19. 8,14,25,46,82,?

A. 138
B. 153
C. 166
D. 139
E. 135

20. 14, 8, 7, 11.5, 22, ?

A. 54
B. 59
C. 56
D. 58
E. 51

21. A box contains 27 marbles some are blue and others are green. If a marble is drawn at random from the box, the probability that it is blue is 1/3. Then how many number of green marbles in the box?


A. 10
B. 15
C. 14
D. 18
E. None of these

22. An employer reduces the number of his employees in the ratio of 7:4 and increases their wages in the ratio 3:5. State whether his bill of total wages increases or decreases and in what ratio.


A. increases 20:21
B. decreases 21:20
C. increases 21:22
D decreases 22:21
E. None of these

23. Rs 6000 becomes Rs 7200 in 3 years at a certain rate of compound interest. What will be the amount received after 9 years? 

A. Rs 11,498
B. Rs 10,352
C. Rs 9,368
D. Rs 10,368
E. None of these

24. A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?


A. 30 mins
B. 25 mins
C. 45 mins
D. 50 mins
E. None of the Above

25. Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 kmph. The second goes at a speed of 8 kmph in the first hour and increases its speed by 1/2 kmph each succeeding hours. After how many hours will the second car overtake the first, if both cars go non stop?


A. 8 hours
B. 7 hours
C. 6 hours
D. 9 hours
E. None of these

26. 1)  x² + 30x + 221 = 0
      2 ) y² – 53y + 196 = 0


A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

27. 1) x² – 82x – 255 = 0
      2) y² – 29y + 208 = 0


A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

28. 1) x² – 33x + 272 = 0
      2) y² – 30y + 224 = 0


A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

29. 1) x² – 30x + 104 = 0
      2) y² – 53y + 702 = 0


A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

30. 1) x² + 11x – 180 = 0
      2) y² + 20y + 91 = 0


A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

Directions(31-35): What approximate value will come in the place of the question mark(?) in the following questions?(You are not expected to calculate the exact value.)

31. 1524.79 * 19.92 + 495.26 = ?

A. 31000
B. 32000
C. 33000
D. 34000
E. 36000

32. 1548.45 + 3065.15 ÷ 15.058 = ?

A. 1650
B. 1750
C. 1850
D. 1950
E. 1550

33. 25*3.25 + 50.4 ÷ 24 = ?

A. 77
B. 66
C. 55
D. 44
E. 60

34. (833.25 – 384.45) ÷ 24 = ?

A. 15.8
B. 16.5
C. 18.7
D. 17.9
E. 17.5

35. 5907 – 1296 ÷ 144 = ? * 8

A. 700.25
B. 658.25
C. 628.25
D. 737.25
E. 630.5

                                         ANSWERS

1. Let the fourth man can do the job in 'x' days.

   Togeher the fraction of work they complete in 1 day = (1/4 + 1/8 + 1/16 + 1/x) =      (7x+16)/16x

   So, they will complete the job in 16x/(7x+16) days.

   Now, according to the question,

   

   16x/(7x+16) = 2

   Solving, we get,

   x = 16 days.

   Thus fourth man's share will be = [(1/16)/(1/2)]*16000 = Rs 2000.

2. Lets assume distance travelled by X before meeting 'x'

    Then distance travelled Y will be (260-x).

   Now, for Train X, its given,

   Time = 2 hrs

   Distance = x km

   Thus, speed will be = x/2 km/hr

   Similarly for Train Y,

   Time = 2 hrs

   Distance = (260-x) km

   Thus speed will be = (260-x)/2 km/hr

Therefore the sum of the speeds of the trains will be,

    = x/2 + (260-x)/2

    = 260/2

    = 130 km/hr. 

3. Lets assume the amount to be mixed at 42 paise/kg be 'x'

    Amount of sugar at 24 paise/kg = 25 kg

Then, 

    Total cost price = Amount * Price = (x*42) + (25*24) = 42x + 600

    Total amount of sugar after mixing = (x+25) kg

    Price of mixed sugar = 40 paisa

Thus, selling price = Total amount * Price = (x+25)*40

Now profit % is 25%, so,

    25/100 = [(x+25)*40 - (42x+600)]/(42x+600)

Solving, we get,

    x = 20 kg.

4. Let the age of father and son be x and y respectively. 

    x + y = 30*2 = 60

    3x = 7y

    x = 7y/3

Putting this in above equation, we get,

    y = 18, thus x = 42

    x – y = 42 – 18 = 24.

5. Speed of train = (960/16)*(70/100) = 42 km/hr.

6. Probability = 8/14 = 4/7.

7. n(E)=HT,TH,HH

    P(E)=3/4

8. Marks in all subjects = 54 + 65 + 89 + 69 + 68 = 345 

   Total maximum marks = 5 * 100 = 500 

   Required percentage =(345/500)*100=69%   

9. Let no of men = x & total population be 100

    Total women = (100-x) 

    Married man = 45x /100    … (i) 

    & married women = 25/100 (100-x)  … (ii)

    From (i) = (ii) 

    x = 500/14

   So, married man = 225 /14

   Married woman = 225/14

   Total married population = men + women = 450/14

   Required % = (450/14)/100 *100 = 450/14% = 32.14%

10. Given, C's marks= 300

      C's % marks = 300*100/400=75%

      B 's% marks = 80%

      A 's% marks =90%

      A 's marks = 90% of 400 = 360

11. Amount spent by PamTech on transport = 5% of Rs. 80000 = Rs. 4000

      Amount spent by RamTech on transport = 10% of Rs. 100000 = Rs. 10000

      Hence, (4000 × 100)/10000 = 40%

12. (45 + 35)/ 200 = 0.4

13. Others for both the companies = Rs. 4000

14. For the category, raw material the difference is maximum 

      = 45000 – 28000 = Rs. 17000.

15. Amount spent by PamTech on salaries = 20% of Rs. 80000 = Rs. 16000

      Amount spent by RamTech on rent = 10% of Rs. 100000 = Rs. 10000

      Required % = 6000/10000*100=60% More

16. 13 * 1 + 1 = 14

      14 * 2 + 2 = 30

      30 * 3 + 3 = 93

17. 11 – 9 = 2

      16 – 11 = 5

      33 – 16 = 17;( 5 – 2 = 3; 17 – 5 = 12(3*4))….

18. 14 – 8 = 6

      25 – 14 = 11

      46 – 25 = 21; 11 – 6 = 5, 21 – 11 = 10….

  

19. 65 – 63 = 2

      74 – 70 = 4

      63 – 61 = 2…..

20. 14 * 0.5 + 1 = 8

      8 * 1 – 1 = 7

      7 * 1.5 + 1 = 11.5 

21. Lets assume no. of blue marbles is 'x'

      xc1/27c1 = 1/3

      x/27=1/3

      x= 27/3 =9

      No of green marbles = Total – (no. of blue marbles) = 27-9 = 18

22. Let initial employees be 7x and then 4x similarly initial wages be 3y and then 5y

      so total wage = 21xy initially and then 20xy

      so wages decreases and ratio = 21:20.

23. 6000[1 + r/100]^3 = 7200

      So [1 + r/100]^3 = 6/5

      So 6000[1 + r/100]^9 = 6000*(6/5)*(6/5)*(6/5) = Rs 10,368.

24. x/6 – (x+5)/12 – (x+5)/15 = 0

      x = 45 mins

25. The second car overtake the first car in x hours

      Distance covered by the first car in x hours = Distance covered by the second car         in  x hours

      10x = x/2[2a + (x-1)d] 

      10x = x/2[2*8 + (x-1)1/2] 

      x = 40 -31 = 9   

26. (x + 13) (x + 17) = 0

      x = – 13, – 17

      y² – 53y + 196 = 0

      y = 49, 4

27. x² – 82x – 255 = 0

      x = 85, -3

      y² – 29y + 208 = 0

      y = 13, 16

28. x² – 33x + 272 = 0

      x = 16, 17

      y² – 30y + 224 = 0

      y = 16, 14

29. x² – 30x + 104 = 0

      x = 26, 4

      y² – 53y + 702 = 0

      y = 26, 27 

30. x² + 11x – 180 = 0

      x = -20, 9

      y² + 20y + 91 = 0

      y = -13, -7

31. A. 31000

32. B. 1750

33. A. 77

34. C. 18.7

35. D. 737.25

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