SOLUTION: Mr. X had a habit of spending money according to dates. i. e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15. One night he calculated total spend

Question 987601: Mr. X had a habit of spending money according to dates. i. e. If date is 19 he was spending Rs.19 and if date is 15, he was spending Rs. 15.
One night he calculated total spending of 5 consecutive days - Monday to Friday and he found that he spent Rs. 61 in 5 days.
So, identify the dates.???
Answer by ikleyn(52807)   (Show Source): You can put this solution on YOUR website!
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Answer. There is only one solution:
              27 and 28 of February and 1, 2, and 3 of March.
              (27 + 28 + 1 + 2 + 3 = 61).

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 of 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 61 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 the the dates 27, 28, 1, 2 and 3 satisfy the condition 27 + 28 + 1 + 2 + 3 = 61.
Next, it is easy to see that there is no other solution.

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