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Day–Date Identification

Introduction

किसी भी तारीख के लिए सप्ताह का दिन निकालना एक सामान्य aptitude कार्य है। यह पैटर्न आपको किसी भी तारीख को सरल गणना या formulaic शॉर्टकट्स से weekday में बदलना सिखाता है - जो कैलेंडर, planning और कई competitive tests में उपयोगी है।

Pattern: Day–Date Identification

Pattern

किसी भी तारीख को weekday में बदलने का तरीका: किसी ज्ञात reference date से कुल दिनों (या odd days) की गिनती करें और उसे 7 से modulo में बदल दें।

Step-by-Step Example

Question

1 January 2020 को सप्ताह का कौन-सा दिन था?

Solution

  1. Step 1: एक सुविधाजनक reference date चुनें

    1 Jan 2000 = Saturday (यह एक commonly याद किया जाने वाला reference है)। हम 1 Jan 2000 से 1 Jan 2020 तक odd days गिनेंगे।

  2. Step 2: पूरी वर्षों की गणना और odd days निकालें

    2000 से 2019 तक कुल 20 वर्ष। इस अवधि में leap years: 2000, 2004, 2008, 2012, 2016 = 5 leap years। Ordinary years = 20 - 5 = 15। Odd days = (15 × 1) + (5 × 2) = 15 + 10 = 25 odd days.

  3. Step 3: Odd days को modulo 7 में बदलें

    25 ÷ 7 → remainder = 25 - 21 = 4 odd days। इसका मतलब weekday reference से 4 दिन आगे शिफ्ट होगा।

  4. Final Answer:

    Wednesday

  5. Quick Check:

    1 Jan 2000 = Saturday → +4 days → Saturday → Sunday (1) → Monday (2) → Tuesday (3) → Wednesday (4) ✅

Quick Variations

1. नज़दीकी reference (जैसे 1 Jan 2010) चुनें ताकि गणना कम हो।

2. तेज़ calculation के लिए month codes या Zeller’s formula का उपयोग करें।

3. एक ही वर्ष की तिथियों के लिए महीनों के odd days गिनें, वर्षों के नहीं।

Trick to Always Use

  • Step 1 → एक याद रहने वाली reference date चुनें (जैसे 1 Jan 2000 या हाल की किसी वर्ष की 1 Jan)।
  • Step 2 → पूरे वर्षों के odd days निकालें (ordinary = 1, leap = 2), फिर महीनों के odd days जोड़ें, और अंत में modulo 7 करें।

Summary

Summary

  • किसी ज्ञात reference date व उसके weekday से शुरुआत करें।
  • गुजरे वर्षों और महीनों को odd days (ordinary = 1, leap = 2) में बदलें और सभी को जोड़ें।
  • कुल odd days को modulo 7 करें।
  • Reference weekday में उतने दिन आगे शिफ्ट करें और weekday प्राप्त करें।

याद रखने के लिए उदाहरण:
1 Jan 2000 = Saturday → 1 Jan 2020 तक 4 odd days → Saturday + 4 = Wednesday.

Practice

(1/5)
1. What day of the week was 1st January 2016?
easy
A. Thursday
B. Friday
C. Saturday
D. Sunday

Solution

  1. Step 1: Choose a reference date

    Take 1 Jan 2000 = Saturday.

  2. Step 2: Count years from 2000 to 2015

    Total = 16 years. Leap years = 2000, 2004, 2008, 2012 = 4. Ordinary = 12. Odd days = (12×1) + (4×2) = 20 → 20 mod 7 = 6.

  3. Step 3: Add 6 days to Saturday

    Saturday + 6 days → Friday.

  4. Final Answer:

    Friday → Option B

  5. Quick Check:

    1 Jan 2016 is known to be Friday ✅
Hint: For every ordinary year add 1 day; for leap year add 2, then reduce modulo 7.
Common Mistakes: Forgetting that 2000 is a leap year (divisible by 400).
2. If 1st January 1995 was Sunday, what day was 1st January 1996?
easy
A. Monday
B. Sunday
C. Tuesday
D. Wednesday

Solution

  1. Step 1: Identify year type

    1995 is an ordinary year (365 days).

  2. Step 2: Find odd days

    365 ÷ 7 leaves remainder 1 → +1 day shift.

  3. Step 3: Apply the shift

    Sunday + 1 = Monday.

  4. Final Answer:

    Monday → Option A

  5. Quick Check:

    Ordinary year moves the date forward by one day → Sunday → Monday.
Hint: Ordinary year → +1 day shift.
Common Mistakes: Using leap-year shift (+2) incorrectly.
3. If 15th August 1947 was Friday, what day was 15th August 1948?
easy
A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

  1. Step 1: Identify year type

    1948 is a leap year, and since the date (15 August) is after February, the span includes Feb 29, 1948.

  2. Step 2: Odd days for leap-year span

    Leap-year span → +2 days.

  3. Step 3: Apply the shift

    Friday + 2 = Sunday.

  4. Final Answer:

    Sunday → Option B

  5. Quick Check:

    Leap-year same-date shift after February is always +2 days.
Hint: If the target date is after Feb in a leap year → +2 days.
Common Mistakes: Adding only +1 instead of +2.
4. Find the day of the week on 26th January 1950 (India’s Republic Day).
medium
A. Wednesday
B. Friday
C. Saturday
D. Thursday

Solution

  1. Step 1: Use reference 1 Jan 1900 = Monday

    We will compute total odd days from 1 Jan 1900 to 26 Jan 1950.

  2. Step 2: Count odd days from 1900 to 1949 (50 years)

    Leap years = 1904,1908,1912,1916,1920,1924,1928,1932,1936,1940,1944,1948 = 12.
    Ordinary years = 50 - 12 = 38.
    Odd days = (12×2) + (38×1) = 62 → 62 mod 7 = 6.

  3. Step 3: Add odd days for 1-25 January 1950

    Days passed before 26 Jan = 25.
    25 mod 7 = 4.

  4. Step 4: Total odd days

    6 (years) + 4 (January days) = 10 → 10 mod 7 = 3.

  5. Step 5: Final weekday

    Reference day = Monday.
    Monday + 3 days = Thursday.

  6. Final Answer:

    Thursday → Option D

  7. Quick Check:

    1 Jan 1900 = Monday → +3 odd days gives Thursday → matches historical record (26 Jan 1950).
Hint: Always use (days passed) mod 7, not the date number mod 7.
Common Mistakes: Using 26 mod 7 instead of 25 mod 7, and miscalculating weekday shifts.
5. If 1st March 2021 was Monday, what day was 1st March 2020?
medium
A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

  1. Step 1: Identify direction

    We are moving one year backward (2021 → 2020).

  2. Step 2: Determine type of year

    2020 is a leap year, so shift backward by 2 days.

  3. Step 3: Apply backward shift

    Monday - 2 = Saturday.

  4. Final Answer:

    Saturday → Option A

  5. Quick Check:

    Leap year backward → -2 days shift ✅
Hint: Backward across leap → -2 days; across ordinary → -1 day.
Common Mistakes: Adding days instead of subtracting when going backward.

Mock Test

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