The birthday of Sandhya falls on 15 August and the birthday of Minu falls on 25 June. If in a certain year Minu had her birthday on a Wednesday, what day of the week was Sandhya's birthday in that same year?

Difficulty: Medium

Correct Answer: Friday

Explanation:


Introduction / Context:
Calendar reasoning questions ask you to move forward or backward through dates and determine corresponding days of the week. Here, you are given two birthdays in the same year and the weekday for one of them. The task is to calculate the day of the week for the other birthday by counting the number of days between the two dates.


Given Data / Assumptions:
- The birthday of Minu is on 25 June. - The birthday of Sandhya is on 15 August of the same year. - In the year considered, 25 June falls on a Wednesday. - We treat the year as a normal year for month lengths, and both dates lie in the same year.


Concept / Approach:
The key approach is to calculate the exact number of days between 25 June and 15 August. Once this difference is known, we find the remainder when dividing by 7, because the day of the week repeats every seven days. By moving forward from Wednesday by this remainder, we obtain the weekday for 15 August. Careful counting of days across June, July, and August is essential.


Step-by-Step Solution:
Step 1: Determine days remaining in June after 25 June. June has 30 days, so there are 30 - 25 = 5 days left in June. Step 2: Count all days in July, which has 31 days. Step 3: Count days in August up to 15 August, which is 15 days. Step 4: Total number of days from 25 June to 15 August is 5 + 31 + 15 = 51 days. Step 5: To find the net shift in weekday, divide 51 by 7. We get 51 = 7 * 7 + 2, so the effective shift is 2 days forward. Step 6: Start from Wednesday, then move two days forward: Wednesday to Thursday is one day, Thursday to Friday is the second day. Step 7: Therefore, 15 August in that year falls on a Friday.


Verification / Alternative check:
As an alternative check, you can mark a short table of weekday shifts. Because 49 days correspond to exactly seven weeks, they do not change the weekday. The remaining 2 days shift the weekday from Wednesday to Friday. This method confirms that any error would have to come from miscounting the number of days between the two birthdays. Since the month lengths used are standard and the arithmetic 5 + 31 + 15 = 51 is correct, the resultant weekday Friday is reliable.


Why Other Options Are Wrong:
Monday: This would correspond to a shift of four days backward from Friday or a different remainder, which does not match the 51 day difference. Tuesday: This would require a shift of five days backward or two days backward from Thursday, which is not supported by the calculation. Saturday: This would correspond to a three day forward shift from Wednesday, which is larger than the remainder of two days.


Common Pitfalls:
A frequent mistake is to include or exclude the starting date incorrectly when counting days, which can change the total by one. Learners also sometimes misremember the number of days in July or June, which leads to a wrong remainder when dividing by seven. Another pitfall is to move in the wrong direction, going backward instead of forward. Writing down the months with their lengths and doing the arithmetic step by step helps avoid these issues.


Final Answer:
The day of the week on Sandhya's birthday in that year was Friday.

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