Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are first given that John worked for 10 hours and that Mary worked for 2 hours less than John. So we can say:
John’s hours = 10
Mary’s hours = 8
We are also given that John and Mary were each given x dollars in advance. We can use this to determine the hourly wage for both Mary and John.
Since (hourly wage)(# of hours) = total paid, we can say that:
hourly wage = (total paid)/(# of hours)
John’s hourly wage = x/10
Mary’s hourly wage = x/8
We are also told that Mary gave John y dollars of her payment so that they would have an equal hourly wage. This means that Mary actually made x – y dollars. Since John received y dollars he now makes x + y dollars. Using this information, the hourly wages of John and Mary are:
Mary’s wage = (x – y)/8
John’s wage = (x + y)/10
Since we are told that the two hourly wages are the same, we can set the hourly wages of John and Mary equal to each other.
(x + y)/10 = (x – y)/8
We can cross multiply and we get:
8x + 8y = 10x – 10y
-2x = -18y
x = 9y
Answer: E
