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On March 1st 2016 , sherry saved ₹ 1. Everyday starting from March 2nd 2016, he save ₹1 more than the previous day . Find the first date after March 1st 2016 at the end of which his total savings will be a perfect square.
  • a)
    17th March 2016
  • b)
    18th March 2016
  • c)
    26th March 2016
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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On March 1st 2016 , sherry saved 1. Everyday starting from March 2nd ...
Understanding Sherry's Savings
Sherry starts saving on March 1st, 2016, with an initial amount of 1 unit. Starting from March 2nd, he saves an additional 1 unit every day. This means his savings for each day can be calculated as follows:
- **March 1st**: 1 unit
- **March 2nd**: 2 units
- **March 3rd**: 3 units
- **March 4th**: 4 units
- ...
- **March n**: n units

Calculating Total Savings
To find the total savings by a specific date, we can use the formula for the sum of the first n natural numbers:
\[ \text{Total Savings} = 1 + 2 + 3 + ... + n = \frac{n(n + 1)}{2} \]
Where n is the total number of days since March 1st.

Perfect Squares
We want to identify the first date after March 1st, 2016, where the total savings becomes a perfect square.

Checking Dates
1. **March 1**: \( \text{Total} = 1 \) (Perfect Square)
2. **March 2**: \( \text{Total} = 1 + 2 = 3 \) (Not a Perfect Square)
3. **March 3**: \( \text{Total} = 1 + 2 + 3 = 6 \) (Not a Perfect Square)
4. **March 4**: \( \text{Total} = 10 \) (Not a Perfect Square)
5. **March 5**: \( \text{Total} = 15 \) (Not a Perfect Square)
6. **March 6**: \( \text{Total} = 21 \) (Not a Perfect Square)
7. **March 7**: \( \text{Total} = 28 \) (Not a Perfect Square)
8. **March 8**: \( \text{Total} = 36 \) (Perfect Square: \(6^2\))
The first date after March 1st when the total savings is a perfect square is **March 8th, 2016**.

Conclusion
Since the options provided do not include March 8th, the correct answer is **None of these** (option 'D').
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Community Answer
On March 1st 2016 , sherry saved 1. Everyday starting from March 2nd ...
According to the question,
Every day adding 1 rs extra to previous day.
Let us assume after n day, total saving will become perfect square.
1 + 2 + 3 + 4 + 5 + 6 +.......................+ tn.
Apply the algebra A.P formula,
sum of total rupees after n days = n(n+1)/2
Hit and trail method, Put the value of n = 2 , 3 , 4, 5 .... and so on to get the perfect square.
If n = 2
n(n+1)/2 = 2 x 3 / 2 = 3 which is not perfect Square.
If n = 3
n(n+1)/2 = 3 x 4 / 2 = 6 which is not perfect Square.
If n = 4
n(n+1)/2 = 4 x 5 / 2 = 10 which is not perfect Square.
If n = 5
n(n+1)/2 = 5 x 6 / 2 = 15 which is not perfect Square.
If n = 6
n(n+1)/2 = 6 x 7 / 2 = 21 which is not perfect Square.
If n = 7
n(n+1)/2 = 7 x 8 / 2 = 28 which is not perfect Square.
If n = 8
n(n+1)/2 = 8 x 9 / 2 = 36 which is perfect Square.
n(n+1)/2 should be a perfect square . The first value of n when this occurs would be for n = 8. thus , on the 8th of March of the required condition would come true.
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On March 1st 2016 , sherry saved 1. Everyday starting from March 2nd 2016, he save 1 more than the previous day . Find the first date after March 1st 2016 at the end of which his total savings will be a perfect square.a)17th March 2016b)18th March 2016c)26th March 2016d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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