In a queue, Vijay is fourteenth from the front and Jack is seventeenth from the end, while Mary is in between Vijay and Jack. If Vijay be ahead of Jack and there be 48 persons in the queue, how many persons are there between Vijay and Mary?

Total students = [ First position of Ganesh + Second position of Rajan ] ?1
Total students = [12 + 20] ? 1 = 31

According to given question,
If the positions of the first and the sixth digits of the group of digits 3 5 9 7 2 8 0 1 6 4 are interchanged.
New number after interchange = 8 5 9 7 2 3 0 1 6 4
Then the positions of the second and the seventh digits are interchanged.
New number after interchange = 8 0 9 7 2 3 5 1 6 4

After interchanging the number becomes as follows: 8 0 9 7 2 3 5 1 6 4

fourth digit from the right end after the rearrangement : 5

According to question,
In a row of boys Akash is fifth from the left
Left 1 - 2 - 3 - 4 - Akash - 6 - 7 - 8 - 9 - 10 - 11 - 12 .................................................................................................................. Right
If Akash is twenty-fifth from the right then
Left 1 - 2 - 3 - 4 - Akash - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 -14 - 15 -16 -17 -18 -19 - 20- 21- 22 - 23- 24- 25 -26 -27 -28 - 29 Right
Nikhil is eleventh from the right.
Left 1 - 2-3 -4 - Akash - 6 -7- 8- 9-10 -11-12- 13-14- 15 -16-17-18 - Nikhil -20-21-22 - 23 - 24 - 25-26 -27- 28- 29 Right

There are (25 ? 11? 1) = 13 boys between Akash and Nikhil.

According to question,
If the positions of the first and the fifth digits of the number 83721569 are interchanged.
After interchange the new number = 13728569
similarly, the positions of the second and the sixth digits are interchanged.
Again after interchange the new number = 15728369

New arrangement of numbers is as follows: 15728369
Hence, third number from right end is 3.

According to the question,
Rajnish is older than Rajesh and Raman.
Rajnish > Rajesh, Raman..........(i)
Ramesh is older than Rajesh but younger than Rajeev.
Rajeev > Ramesh > Rajesh........(ii)
Raman is older than Rajeev.
Raman >Rajeev.......................(iii)
Combining all, we get
Rajinish > Raman > Rajeev > Ramesh > Rajesh

After exchanging positions, Bhusan becomes fifteenth instead of seventh from the left, it means there are 7 students between them. So Motilal's position from the right will become twelfth. [i.e., (15 ? 7) + 4 = 12]

The possible date of birth of Ana according to Adi are 21st and 22nd September. But according to his father Ana's date of birth should be 22nd and 23rd September. Now after both conclusion there is 22nd September common date, so answer is that (b).

Failed Students
= [ Total students ] ? [ (Anmol's position from upwards) + (Anmol's position from downwards) ? 1 ]
= 45 ? [(11 + 15) ? 1] = 20

If the first working day happened to be Tuesday then 8th, 15th, 22nd and 29th of the month will be Tuesday. Hence, the last day of the month will be Wednesday (since, number of days in the month is 30). Thus, the next casual leave will be on Thursday.

Anil reached the place on Friday and he was three days earlier than the scheduled day.
Therefore, the scheduled day = Friday + 3 days = Monday
If he had reached on Sunday then he would have earlier than one day.
i.e. Monday - one day = Sunday