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?

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