Question

In a school, 156 passed geography or history. 75 students passed both subjects. If nine more passed geography as passed history, how many students passed each subjects?

Answer 1

Make a Venn diagram
passing history ---- x
passing geography --- x+9

put 75 in the intersection of both circles.
put x - 75 in the "history only " part of the history circle
put x+9 - 75 in the "geography only" part of the geography circle

x-75 + 75 + x-9+75 = 156
2x = 222
x = 111

So 111 passed history, and 120 passed geography .

Proof:
number who passed history only = 111-75 = 36
number who passed only geography = 120-75 = 45
number who passed both = 75
total of the parts of the Venn diagram = 36+45+75 = 156

the bot should have know that its answer is wrong since the
number of geography was to be 9 more than history.
It has geography less than history !!!

x + x+9 - 75 = 156
2x = 222
x = 111

111 passed history, and 120 passed geography

Answer 2

"....for providing an alternate solution using a Venn diagram!" ??????
you should have added " and the correct solution".

You didn't even admit that your solution was totally wrong !!!
Your first clue that you were wrong should have been when you ended up with a fractional student, lol