df1:
Date       Fruit  Num  Color
2013-11-24 Banana 2 Yellow
2013-11-24 Orange  8 Orange
2013-11-24 Apple   7 Green
2013-11-24 Celery 10 Green

df2:
Date       Fruit  Num  Color
2013-11-24 Banana 22 Yellow
2013-11-24 Orange  8 Orange
2013-11-24 Apple   7 Green
2013-11-24 Celery 1 Green

library(dplyr)
test <- rbind(df1, df2)
test2 <- test %>%
  group_by(Date) %>%
summarise(max = max(.))

new.df:
Date       Fruit  Num  Color
2013-11-24 Banana 22 Yellow
2013-11-24 Orange  8 Orange
2013-11-24 Apple   7 Green
2013-11-24 Celery 10 Green