Solutions for Ranking sequence

1.   Kanmani rank from top =s1, bottom=s2

Total boys who passed exam= (s1+s2-1) = (16 + 29 - 1) = 44
Total number of boys in the class = 44(passed) + 6(did not participate)
 +5(failed) = 55.

2. Murugan rank from left =s1=6,

Prassanna rank from right =s2=10

Boys who were in between them =8

So Murugan would rank s2=10+9=19^th from right

Total number of boys in the class = (s1+s2-1) = (6 + 19 - 1) = 24

3.Nithya rank from right =9,

Suganya rank from left =10

They exchange places, so Nityas new position is the same as Sugunya’s earlier position. This position is 17th from the right and 10th from the left. Therefore Number of girls in the row = (17 + 10 - 1) = 26.

4. Arun rank from left =5,

Suresh rank from right =6

Arun and Suresh interchange places, so Arun’s new position(13th from left) is the same as Suresh’s earlier position (6th from right).
So, number of children in the queue = (13 + 6 - 1) = 18.
Suresh’s new position is the same as Arun's earlier position fifth from left. Therefore Suresh’s position from the right = (18 – 5 + 1) = 14th.

5. Sathish is 17th from the last

Vimal is 7 ranks ahead of Sathish.

So, Vimal is 24th from the last.
Vimal’s rank from the start. = (39 – 24+1) = 16.

6. Number of students =35

Kamal 7^th from bottom Sunil 9^th from top

Kamal from top => (35=7-x+1) =>27

So the difference between sunil and Kamal is 27-9=18

Manoj is between them, so Kamal is 10th from Manoj.

7.    Ashok rank from left =15, Sakhti rank from right =7.They interchange places, so Sakhti’s new position (15th from right) which was Ashok’s earlier position (15th from left)
so, number of children in the queue = (15 +15 - 1) = 29.

8.    Ramya’s rank from left =5, Priya’s rank from right =6.They interchange places, so Ramya’s new position (13th from left) which was Ashok’s earlier position (6th from right)
so, number of children = (13 +6 - 1) = 18.

Now, Priya’s new position is Ramya’s earlier position which is 5th from the left.
Number of girls to the right of Priya = (18 - 5) = 13.
So, Priya’s new position is 14th from the right.

9.    A is 15^th from left, B is 4rth from right and  boys between A and B

Number of boys in the row = (15 + 4 + 3 ) = 22.
C is just left of A. So, C is 14th from the left end and 9th from the right end of the row.

10. Viji is 14^th from front

Jack is 17^th from end

Total 48members

Number of persons between Viji and Jack = 48 - (14 + 17) = 17.
Now, Mary lies in middle of these 17 persons i.e., at the 8^th position.
So, number of persons between Viji and Mary = 7.

11. Mahi 9^th from top, 38^th from bottom

     Total students = (s1+s2-1) => (38 +9 - 1) = 46 students.

12. Pallavi is 21st from right and Reena is 10th to the left of Pallavi. 

     So, Reena is 31st from right.
     Malini is 4th to the right of Reena. 
     So, Malini is 27th from the right.
     Also, Malini is 17th from the left.
     Therefore number of girls in the row = (27 + 17-1 ) = 43.

13. Sugan 16^th from top, 49^th from bottom

     Total students = (s1+s2-1) => (15 +49 - 1) = 64 students.

 14. Number of students = 49 

      Rajan is 18^th from top =s1

      49=18+x-1=> x=32.

      Rajan is 32nd from the last.

15. A is 15^th from left, B is 4rth from right and  boys between A and B

Number of boys in the row = (15 + 4 + 3) = 22.
C is just left of A. So, C is 14th from the left end and 9th from the right.

Solutions for Coding and Decoding

1.ENTRY = 12345

        STEADY=931785

        TENANT=?

         From the above two words T=3, E=1, N=2, A=7, N=2, T=3

         312723

     2.      DAWN=FDAS

      ????=WIND

      D=4 A=1 W=23 N=14 and F=6 D=4 A=1 S=19

      So difference is gradually increasing 2,3,4,5

      W=23 I=9 N=14 D=4

       23-2=21    U

       9-3=6        F    

       14-4=10    J

       4-5=25      Y

       UFJY=WIND

     3.      Football=cricket

    Cricket=basketball

    Basketball=volleyball

    Volleyball=khokho

    Khokho=cricket

    A ball less game=khokho here khokho is Cricket

4.      Life is good = KUI ENB KAJ

Live your life=ENB KIR JIN

So life = ENB

5.      BUCKET: ACTVBDJLDFSU

      Previous and next letter of each alphabet

      BONUS: ACNPMOTVRT

6.    Z=52,  ACT=48 
 ð  A=2, C=6, T=40

 Double value for each alphabet

 BAT => B=4, A=2, T=40 =>46

7.      NAIDU = 51943

      PRABHA=791281

      Addition of values of each digit are added for example N=14 =>1+4=5

      =>LAXMAN=?

       L=12=1+2=3

       A=1

       X=24=2+4=6

       M=13=1+3=4

       A=1

       N=14=1+4=5

       So LAXMAN=316415

8.    HASAN=SZHZM

     PRASU=?

    Opposite letters so PRASU=KIZHF

9.   LONDON=QNBLPQ

    DENCIL=? 

    LONDON is coded with +2,+2,-2,-2,+2,+2

    That is NQLBQP

    Then swap two two letters in a order

    That is QNBLPQ

    Similarly DENCIL is coded as GFALNK

10.  DELHI=CCIDD

      BOMBAY=?

      Difference 1, 2, 3, 4, 5

      B=>2 -1=A

      O=>15-2=M

      M=>13-3=J

      B=>2-4=X

      A=>1-5=V

      Y=>25-6=S

       =>AMJXVS

11.  ROAD=URDG

      SWAN=?

      Difference is 3

      So S+3=V

      W+3=Z

      A+3=D

      N+3=Q

      So VZDQ

12.  Each letter is given odd value then HOTEL=?

      H=2*8-1=15

      O=2*15-1=29

      T=2*20-1=39

      E=2*5-1=9

      L=2*12-1=23

      So 15+29+39+9+23=115

13.  BASIC=DDULE

      +2, +3, +2, +3, +2

      LEADER=?

      L+2=N

      E+3=H

      A+2=C

      D+3=G

      E+2=G

      R+3=U
 ð  NHCGGU

14.  TERMINAL=SDQLJOBM

      -1,-1,-1,-1,+1,+1,+1,+1

      CREDIBLE=BQDCJCMF

15.  YEB,WFD,UHG,SKI,____

      Y-2=W, W-2=U, U-2=S, S-2=Q

      E+1=F, F+2=H, H+3=K, K+4=O

      B+2=D, D+4=G, G+2=I, I+4=L

      ð  QOL

Solutions for Number series

1.      544,509,474,439,___

544-509=35

509-474=35

474-439=35

439-x=35

So, 439-35=404

2.      2,6,18,54,___

2*3=6

6*3=18

18*3=54

54*3=162

3.      8,6,9,23,87,___

8*1-2=6

6*2-3=9

9*3-4=23

23*4-5=87

87*5-6=429

4.      1,9,17,33,49,73,___

1+8=9

9+8=17

17+16=33

33+16=49

49+24=73

73+24=97

5.      5,9,17,29,45,___

5+4=9

9+8=17

17+12=29

29+16=45

45+20=65

6.      121,225,361,___

121= 11²

225= 15²

361= 19²

The diff of squares are 4

So 23²= 529

7.      0,2,8,14,___,34

1*1-1=0

2*2-2=2

3*3-1=8

4*4-2=14

5*5-1=24

6*6-2=34

8.       3,6,18,72,___

3*2=6

6*3=18

18*4=72

72*5=360

9.      2,15,41,80,__

2+13=15

15+26=41

41+39=80

80+52=132

10.  7: 56:: 9:?

7*8=56

9*10=90

11.  10: 26:: 50:?

3*3+1=10

5*5+1=26

7*7+1=50

9*9+1=82

12.  28:39 ::52:?

5*5+3=28

6*6+3=39

7*7+3=52

8*8+3=67

13.  6522: 114:: 2859: ?

6522 => 6+5=11, 2+2=4 =>114

2859=> 2+8=10, 5+9=>14 =>1014

14.  4,8,9,16,___

All are Perfect squares Except  8

( 2²=4, 3²=9^,, 4² = 16)

                                                                                              

15.  37,47,57,67 Odd man out

57 is not prime where as others are prime

16.  24,60,124,210 Odd man out

Except 124 others are multiples of 3

17.  144,169,256,324 Odd man out

144=12²

169=13²

256=16²

324=18²

Here except 13 others are even numbers, so 169

18.  121, 441, 991, 1681 Odd man out

Except 991 others are squares

19.  125,343,729,2197 Odd man out

5³=125

7³=343

9³=729

13³=2197

Except 9 others are prime so 729

20.  3587: 1556:: 8734:?

3*5=15

8*7=56

Similarly 8*7=56, 3*4=12 so 5612

21.  2,7,24,77,___

3^1-1=2

3^2-2=7

3^3-3=24

3^4-4=77

3^5-5=238

22.  3,4.5,9,22.5,___

3*1.5=4.5

4.5*2=9

9*2.5=22.5

22.5*3=67.5

23.  9,19,40,83,__

9*2+1=19

19*2+2=40

40*2+3=83

83*2+4=170

24.  55,19,44,12,33,7,___

Alternative series 55 – 44 – 33 - ?

Difference 11 so 33-11 =22

25.  46: 574 :: 56: ?

4*6=24

24*24=574

So 5*6= 30

30*30 = 900

Solutions for Time and Distance

 1.  (Difference between speeds/Maximum Speed)

       = (54kmph-45kmph)/ (54kmph) = (9/54) hrs

       = (9/54)*60mins= 10 minutes

2.  Distance = speed * time

     Given distance = (100+400) meters

     Speed=90kmph= (90*5/18) =25mps

     500 = 25 * time

     Time= 500/25 = 20 sec

3.  (2*a*b)/ (a-b) since same direction

     = (2*9*6)/ (9-6) = 108/3 =36 seconds

4. Train A starts at 9AM and travels at 60kmph

     In 2hrs i.e. by 11AM it travels 120kms

    Then train B starts with 100kmph

    Time to meet=distance/relative speed

     =120/ (100-60) = 120/40 = 3hrs

    So 11AM+3hrs = 2PM

5.  (2*a*b)/ (a+b) since opposite direction

     = (2*10*15)/ (15+10)

     = 300/25 =12 seconds

6.  A travels for 3hrs at 80kmph =240km

     B travels at 110kmph

     Time to meet=distance/relative speed

      =240/ (110-80) = 240/30 = 8hrs

      So distance =8*110km = 880km

7.  (Product of 2 speeds / difference of speeds)*time in hours

      = (30*40/40-30)*(15/60)

      = (1200*15/600) = 30kms

 8.  Distance= (total time * product of speeds)/ sum of speeds

     = (5*3*2)/ (3+2) =6km

    So the distance between school and village is 12/2=6kms

9.  (Product of 2 speeds / difference of speeds)*time in hours

     = (10*12/2)(10/60)

     = (120*10/120) = 10kms

10. Distance = (2*(time)*speed1 * speed2)/ (speed1+speed2)

      Distance= (2*10*21*24)/ (21+24)

      Distance=224km

11. Distance= 120 km

     Sum of speeds = (18+12) = 30kmph

     Therefore time =distance/speed

     =120/30 =4hrs

     So the dogs travels 25*4=100km

12. Distance=200meters

      Speed=72kmph= (72*5/18) =20 mps

      Time= distance/speed =200/20=10sec

13. Speed ratio for car: bus= 3:4

      So Time ratio car: bus = 4:3

      Given time of car is 24minutes =>4*x= 24 so x=6

      So time for bus =3*x =3*6 =18minutes

14.  P travels for 4hrs at 40kmps speed so 160km of distance is covered

       Given total distance = 340 so 340-160=180kms

       To travel 180kms the time taken = distance/sum of speeds

        =180/ (40+50)= 2hrs

       So 10AM + 2hrs =12PM

15.  Extra travelled distance*(sum of speeds/difference of speeds)

       = (180*175/15)

       =2100km

Solutions for Ages

1.       Consider  fathers age= f ,sons age = s

       Given f=3*s +s = 4s           ----1

       f+8 =5/2 *(s+8)                  ----2

       f+16=x *(s+16)

      From 1 and 2 we can say that

      4s+8=5/2(s+8) => (4s+8)*2 = 5s+40

      => 8s+16=5s+40 =>3s=24 =>s=8

     Therefore f=4*8=32 => f+16= 48 and s+16=24

      48 = x *24 =>x= 48/24 => 2 times

2.      Consider age of younger child = x

      Then( x)+(x+3)+(x+6)+(x+9)+(x+12)=50

       5x+30=50 => 5x=20 => X=4

      Therefore youngest child is 4years

3.      F=38 and F=2s => s=19

      Sons age before 5 years = 19-5 = 14years

4.      A=B+2

      B=2C => C = B/2

      A+B+C= 27 =>B+2+B+B/2=27 => B=10

5.      S: A=5: 4 => S=5X ,A=4X

      S+3: A+3=11:9 => S+3=11Y, A+3=9Y

      5X=11Y-3, 4X=9Y-3 Solving them we get y=3

      A+3=9Y => A=9*3-3=27-3=24

6.      M=24+S and M+2=2(S+2)

      Solving them 2S+2=24+S => S=22Years

7.   K-6: S-6=6: 5 => K=6X+6, S=5X+6

      K+4: S+4=11: 10=> K=11Y-4, S=10Y-4

      =>6X-11Y+10=0, 5X-10Y+10=0

      Solving them we get Y=2

      S=10Y-4 = 10*2-4 = 20-4 =16Years

8.  F+S=60

     F-6=5(S-6) =>F-6=5S-30 => F=5S-24

     From the above two equations 5S-24+S=60 => 6S=84 =>S =14

     Therefore after six years S=14+6=20years

9.   A: D = 4:3 =>A= 4X B=3X

      A+6=26 => A=20

      20=4X So X=5 Therefore D=3*5=15 Years

10.  S=R-7

       S: R=7:9 => S=7X, R=9X

       7X=9X-7 =>X=7/2

       S= (7)*(7/2) = 24.5Years

11.  A: B: C= 4: 7: 9 
       => A=4X, B=7X, C=9X

        (A-8) + (B-8) + (C-8) = 56 => A+B+C=80

        4X+7X+9X=80 => X=4

        So A = 4*4 = 16, B = 7*4 = 28, C = 9*4 = 36

12.  F= 38+A

       M=36+B

       B=A-4 => M= 36+A-4 => M=32+A

       So F-M = 38+A-32-A =6Years

13.  P = (2/5)*M => 5P=2M

       (P+8)=1/2(M+8) => 2P+16=M+8 => 2P+8=M

       Solving them we get 5P=2(2P+8) => P=16 So M=16*5/2 =40Years

14. Data not sufficient to solve

15.  F-10 =3(S-10) => F=3S-20

       F+10=2(S+10) => F=2S+10                                                                                                              

   ð  3S-20=2S+10 =>S=30 And F=70

   ð  So F: S= 7:3