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I have a math question. In our bachelor room our water bill is 276. It is a bill for 31 days. But out of this 15 people, only 12 people used water for 31 days. one went for vacation after 20 days that means he drank only 20 days. another drank only 25 days and third one drank only 26 days. In this case how to divide the bill equal to what they drank. I need the answer to be applied in excel so no a+b=x type answer. Only addition, divide and multiplication, can you find the answer please

*How I did it is: 276/31/15=0.59 *So full time 12 people’s share= 12X0.59X31=219.48 *20 day guy’s share=11.87 *25 day guy’s share=14.84 *26 day guy’s share=15.43

*So the total is 261.62 *Difference is 14.38 *My question, should I divide this 14.38 with all 15 friends or 12 friends only

Muhamad Sadik
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    Hint: try to use the daily cost of water as variable – MysteryGuy Sep 04 '17 at 12:16
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    If this is a serious question --- if you're really trying to allocate daily costs of water use among 15 people based on their daily presence/absence, rather than it being a weird homework problem or something --- you're probably operating at the wrong scale. What if Eddie drinks a lot and Tommy drinks almost nothing? What if Eddie fllushes the toilet more often? What you're going to end up with, in your current plan, may be very precise, but not at all accurate. – John Hughes Sep 04 '17 at 12:22
  • Yes, it is a serious question, I know it is not accurate, but let's please find the amount of shares by day of used, not by gulp – Muhamad Sadik Sep 04 '17 at 12:30

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Let us say: the $12$ full time people each pay $A$.

Fairness suggests that a person who stayed $N$ days should pay $\frac N{31}\times A$. Thus we have $$276= 12A +\frac {20}{31}\times A +\frac {25}{31}\times A +\frac {26}{31}\times A \approx 14.29\times A$$

This implies that $\boxed {A = 19.314}$

lulu
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  • What about others sir, those who drank only 20 days and 25 and 26? – Muhamad Sadik Sep 04 '17 at 12:28
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    As I said, if someone stays $N$ days then they pay $\frac {N}{31}\times A$. That's what I'm calling "fair" here. To be sure, that's subjective...somebody else could have a different notion of fair. – lulu Sep 04 '17 at 12:30
  • @MuhamadSadik This and Jaroslaw's answer are the same. With the data available, it is the only sensible answer other than ignore how long they were there. An argument that a straight split is fair could be made. I guess that you cannot suspend the water service for arbitrary short periods. While away, they are paying for the convenience of the water being available when they return. – badjohn Sep 04 '17 at 12:40
  • @badjohn: yes, a fixed quota of the bill should be deducted from the total and paid equally by all 15. – G Cab Sep 04 '17 at 14:01
  • @GCab I actually only suggested the extremes: the sharing proposed by Jaroslaw and Lulu or a straight split but that is another level of sophistication. The bill may even support it with a fixed component and a usage related component. Nonetheless, I would personally argue for a straight split. So, I pay too much (in a sense) when I am on vacation but some other time you are on vacation. It might not balance exactly but the usage when all are home also might not balance. Why worry about one "unfairness" and not the other. – badjohn Sep 04 '17 at 14:35
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If we denote the cost of one unit of water by $x$ (where cost of one unit of water is the cost of drinking water by one person by one day), we have: $$(20+25+26+12\cdot 31) x = 276$$ Thus $$x=\frac{276}{443}$$ So if one person had been drinking water by $k$ days, he'll pay for it $$k\cdot \frac{276}{443}$$

Jaroslaw Matlak
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  • I found the formula above is very convenient to find the answer to my question, How can I mark this as best answer or how can I give points, please let me know, I am new here – Muhamad Sadik Sep 04 '17 at 14:48
  • @MuhamadSadik - if You think, that the answer is useful, you can click the up arrow to give it an upvote. You can also accept the answer by clicking the gray check symbol below the votes - it will change to green. – Jaroslaw Matlak Sep 04 '17 at 15:14