All questions of Clock & Calender for RRB NTPC/ASM/CA/TA Exam

Explanation:

A Leap Year in 1895:
- A leap year is a year that is evenly divisible by 4, except for years that are evenly divisible by 100 but not by 400.
- In 1895, the calendar followed the standard leap year rules, so it had 366 days.

Calendar Matching with Year X:
- To find a possible value of X that has the same calendar as 1895, we need to look for a year that is also a leap year.
- The leap years are generally every 4 years, so we need to find a year that is 4 years away from 1895.

Possible Value of X:
- The year that is 4 years after 1895 is 1899 (1895 + 4 = 1899).
- Since 1899 is a leap year (divisible by 4), it will have the same calendar as 1895.
- Therefore, a possible value of X is 1899.

Conclusion:
- Option 'a) 1901' is incorrect because it is not a leap year.
- Option 'b) 1900' is incorrect because it is not 4 years after 1895.
- Option 'c) 1902' is incorrect because it is not a leap year.
- Option 'd) 1903' is incorrect because it is not 4 years after 1895.
- The correct answer is option 'a) 1901' as it is 4 years after 1895 and a leap year.

Explanation:

To determine the day of the week for August 31, 1961, we need to calculate the number of days between August 28, 1946, and August 31, 1961.

Step 1: Calculate the number of years between the two dates
Since we need to calculate the number of days, we will consider the leap years as well.

Number of leap years between 1946 and 1961 = (Number of leap years before 1961) - (Number of leap years before 1946)
To calculate the number of leap years before a given year, we use the formula:
Number of leap years = (year / 4) - (year / 100) + (year / 400)

Number of leap years before 1961 = (1961 / 4) - (1961 / 100) + (1961 / 400) = 490 - 19 + 4 = 475
Number of leap years before 1946 = (1946 / 4) - (1946 / 100) + (1946 / 400) = 486 - 19 + 4 = 471

Number of leap years between 1946 and 1961 = 475 - 471 = 4

Number of non-leap years between 1946 and 1961 = (1961 - 1946) - Number of leap years between 1946 and 1961 = 15 - 4 = 11

Step 2: Calculate the total number of days between the two dates
Number of days = (Number of leap years * 366) + (Number of non-leap years * 365) + (Number of days from August 28 to August 31)

Number of days = (4 * 366) + (11 * 365) + 3 = 1464 + 4015 + 3 = 5482

Step 3: Determine the day of the week
Since we know that August 28, 1946, was a Wednesday, we can calculate the day of the week for August 31, 1961, by finding the remainder when the total number of days is divided by 7.

5482 ÷ 7 = 826 remainder 4

Since August 28, 1946, was a Wednesday (represented by 0), adding the remainder 4 to 0 gives us a total of 4.

Conclusion:
Therefore, August 31, 1961, was a Thursday.

Explanation:

Calculating the number of days between 15th March 1816 and 15th April 1916:
- From 15th March 1816 to 15th March 1916, it is 100 years.
- From 15th March 1916 to 15th April 1916, it is 31 days (including both the start and end dates).

Calculating the total number of days:
- 100 years have 25 leap years and 75 common years (since every fourth year is a leap year except for centuries not divisible by 400).
- So, there are 25 * 2 + 75 * 1 = 125 extra days from leap years.
- Total days = 100 years * 365 days/year + 125 leap days = 36525 days + 125 days = 36650 days.

Calculating the day of the week:
- Since 15th March 1816 was a Friday, adding 36650 days to it will lead us to the day of the week on 15th April 1916.

Conclusion:
- As the number of days is a multiple of 7 (36650 = 5235 * 7), the day of the week will be the same as it was on 15th March 1816.
- Therefore, 15th April 1916 will also be a Saturday.

Analysis:
To solve this problem, we need to determine the number of days between 2016 and the year in which Mohan celebrates his birthday on a Wednesday. We can then divide this number by 7 to find the number of weeks, and add the remainder to Friday to determine the day of the week of Mohan's birthday in that year.

1. Number of days between 2016 and the year in which Mohan celebrates his birthday on a Wednesday:
Since Mohan did not celebrate his birthday in January or February, we need to consider the period from March to December in each year.
- From March to December in 2016, there are 10 months * 31 days = 310 days.
- In each subsequent year, there are 365 days.
- Therefore, the number of days between 2016 and the year in which Mohan celebrates his birthday on a Wednesday can be expressed as 310 + 365n, where n is the number of years.

2. Number of weeks between 2016 and the year in which Mohan celebrates his birthday on a Wednesday:
To find the number of weeks, we divide the number of days by 7 and take the integer part of the result.
- Number of weeks = floor((310 + 365n) / 7).

3. Remainder:
To determine the day of the week of Mohan's birthday in the year he celebrates it on a Wednesday, we need to find the remainder when the number of days is divided by 7.
- Remainder = (310 + 365n) % 7.

4. Determining the first year:
We need to find the smallest value of n for which the remainder is 2 (Wednesday).
- By trying different values of n, we find that 2020 is the first year after 2016 when Mohan will celebrate his birthday on a Wednesday.

Conclusion:
The first year after 2016 when Mohan will celebrate his birthday on a Wednesday is 2020.