Analysis and solution: This question has a complex quantitative relationship, and it is generally answered by the idea of fractional application. But we can also answer by reasoning.

Because after running away a ram, the number ratio of ram to ewe is 9: 7. After a while, the escaped ram returned to the flock, but ran away from another ewe. At this time, the number ratio of ram to ewe is 7: 5.

That is to say, the total number of sheep has not changed before and after the rams and ewes fled twice respectively. After a ram ran away, the ratio of ram to ewe was 9∶7, 9+7 =16; When the ram returned to the flock, but ran away with a ewe, the number ratio of ram and ewe was 7∶5, 7+5 = 12.

The least common multiple of 12 and 16 is 48. So, before and after a ram and a ewe escaped twice, the total number of sheep was 48, and the number of this group of sheep was:

48+ 1 = 49 (only).