Question 992162: one person has habbit of spending same no. of rupees as per the date on that day.if he spend 63 rupees in 5 days which were those days
Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website! .
Hello,
your formulation is not exactly correct. You forgot to mention that these 5 days were the consecutive days. So I place 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 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 for the similar problem was placed in the lesson Spending money according to dates in this site couple of days ago.
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