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 Domestic Complications (Posted on 2002-07-25)

Smith, Jones and Brown were great friends. After Brown's wife died, his niece kept house for him. Smith was also a widower, and lived with his daughter. When Jones got married, he and his wife suggested that they all live together. Each one of the party (male and female) was to contribute \$25.00 on the first of the month for household expenses, and what remained at the end of the month was to be equally divided.

The first month's expenses were \$92.00. When the remainder was distributed, each received an even number of dollars without fractions. How much money did each receive, and why?

 See The Solution Submitted by Happy Rating: 3.6250 (16 votes)

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 Solution To The Problem Comment 5 of 5 |

Apparently, the total number of persons is 5.
This would require 5*25 - 92 = \$ 33 to be evenly distributed among the, with each person receiving \$ 33/4 = \$ 8.25, which is not a whole number of dollars and thus a contradiction.

Accordingly, at least one of the five persons must possess a dual identity to bring down the number of persons from five.

Upon closer examination, we observe that only Mrs. Jones can have a dual identity, as Mr. Jones' wife and another as as Mr. Brown's niece.

This brings down the total number of persond to four.

Consequently, each person would now receive \$ (25*4 - 92)/4 = \$ 2.

Edited on April 17, 2007, 11:39 am
 Posted by K Sengupta on 2007-04-10 15:44:32

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