Understanding the Date Calculation Problem

The question asks us to find the date that is 554 days after 25^th January 2015. This involves calculating forward in the calendar, accounting for the varying number of days in each month and whether a year is a leap year.

Arzoo was born on \(\text{25}^{\text{th}} \text{ January } 2015\). Aastha was born 554 days later. We need to determine Aastha's birth date.

Step-by-Step Calculation of the Future Date

We start counting the 554 days from the day after Arzoo's birth date, i.e., from January 26^th, 2015.

Step 1: Count Days Remaining in the Year 2015

First, let's calculate the number of days from January 26^th, 2015, until the end of 2015.

• Days remaining in January 2015: \(31 - 25 = 6\) days (Jan 26 to Jan 31)
• Number of days in months from February to December in 2015:
  • February (2015 is not a leap year): 28 days
  • March: 31 days
  • April: 30 days
  • May: 31 days
  • June: 30 days
  • July: 31 days
  • August: 31 days
  • September: 30 days
  • October: 31 days
  • November: 30 days
  • December: 31 days

Total days remaining in 2015 (from Jan 26 to Dec 31):

\(6 (\text{Jan}) + 28 (\text{Feb}) + 31 (\text{Mar}) + 30 (\text{Apr}) + 31 (\text{May}) + 30 (\text{Jun}) + 31 (\text{Jul}) + 31 (\text{Aug}) + 30 (\text{Sep}) + 31 (\text{Oct}) + 30 (\text{Nov}) + 31 (\text{Dec}) = 346\) days.

So, 346 days pass from Jan 26, 2015, to Dec 31, 2015.

Step 2: Calculate Remaining Days to Count in the Next Year (2016)

We need to add a total of 554 days. We have used 346 days in 2015. The number of days remaining to count is:

\(554 (\text{Total days}) - 346 (\text{Days in 2015}) = 208\) days.

These remaining 208 days will fall in the year 2016.

Step 3: Count 208 Days into the Year 2016

We now count 208 days from the beginning of 2016 (January 1^st). We need to remember that 2016 is a leap year because it is divisible by 4 (\(2016 \div 4 = 504\)), so February has 29 days.

Let's accumulate the days month by month in 2016:

After counting days up to the end of June 2016, we have accumulated 182 days in 2016. We need a total of 208 days in 2016. The number of additional days needed in July is:

\(208 (\text{Target days in 2016}) - 182 (\text{Days up to end of June}) = 26\) days.

So, the 208^th day of 2016 is the 26^th day of July. This corresponds to the date 26^th July 2016.

Conclusion: Aastha's Birth Date

Based on the detailed calculation of adding 554 days starting from January 25, 2015, Aastha's birth date is determined by counting 346 days in 2015 (from Jan 26) and then counting the remaining 208 days into 2016. This process leads to the date 26^th July 2016.

Reviewing the provided options, Aastha was born on 1^st August 2016.

Revision Table: Key Date Calculation Concepts

Additional Information: Calendar Math

Date calculations are common in various quantitative aptitude problems. Understanding the structure of the calendar, including the number of days in each month and the rules for leap years, is crucial. When adding a large number of days, it's efficient to count the remaining days in the current year, then full subsequent years (if any), and finally count the remaining days into the target year month by month.

Always be careful when crossing year boundaries, especially into or out of a leap year, as this affects the number of days in February and the total days in the year (365 or 366).