SOLUTION: A man The day on which you Rupees had a habit of spending less (Ex. 18 Table 18 Rs.) Once it is spending Rs 63 for 5 consecutive days So tell me, He was 5 dates on what

Question 993339: A man
The day on which you
Rupees had a habit of spending less
(Ex. 18 Table 18 Rs.)
Once it is spending Rs 63 for 5 consecutive days
So tell me,
He was 5 dates on what?
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
I am placing here the exact formulation and then the solution.
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Mr. X had a habit of spending money according to dates. For example, if date was 19 he was spending 19 rupees, and if date was 15 he was spending 15 rupees.
One night he calculated total spending of 5 consecutive days - Monday to Friday, and he found that he spent 63 rupees in 5 days.
So, identify the dates. (Assume that everyday spending is integer number of rupees).
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Answer. There is only one solution:
              28 and 29 of February of a leap-year and 1, 2, and 3 of March.
              (28 + 29 + 1 + 2 + 3 = 63).

Solution

If these days would be inside one month, then the dates are (x-2), (x-1), x, (x+1) and (x+2), where x is the date in the middle of 5 days.
Then the sum must be multiple of 5, since

(x-2) + (x-1) + x + (x+1) + (x+2) = 5x.

But the integer 63 is not multiple of 5. Contradiction.

Hence, the dates are partly the end of some month and the beginning of the next month.

Then, it is easy to check that the dates 28, 29, 1, 2 and 3 satisfy the condition 28 + 29 + 1 + 2 + 3 = 63.
Next, it is easy to check that there is no other solution.

The solution of this problem was placed in this forum one week ago
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.992162.html .

The solution for the similar problem was placed in the lesson Spending money according to dates in this site couple of weeks ago.

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