Adi remember that his sister Ana's date of birth falls after 20th September but before 23rd September, while his father remember that Ana's birthday falls after 21st and before 24th September. What is the correct date of birth of Ana?

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]

Number of persons between Vijay and Jack = 48 ? (14 + 17) = 17
Now, Mary lies in middle of these 17 persons i.e, at the eighth position.
So, number of persons between Vijay and Mary = 7.

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.

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

Here , Day before yesterday was Sunday.
Therefore, today is Tuesday.
Day after tomorrow will be Thursday.
? Thursday + 3 days = Sunday
Hence , required day will be Sunday .

Given that :- Friday ? 2 days earlier
Therefore, scheduled day = Friday + 2 days = Sunday,
Sunday + 3 days = Wednesday
Therefore, I would have been late by 4 days including Sunday.