If there are 60 teachers of that group of 60 teachers 23 tea

If there are 60 teachers, of that group of 60 teachers, 23 teach atleast one math course and 36 teach atleast one social studies course. If 85% of the teachers teach math or social studies, how many of the teachers teach social studies but not math?

Solution

As 65% of 60 = 51, then 51 teach math or social studies.

As

N(Math or Soc) = N(Math) + N(Soc) - N(Math and Soc)

51 = 23 + 36 - N(math and Soc)

N(math or soc) = 8

Thus, as

N(Math only) = N(Math) - N(math and soc)

Then

N(Math only) = 23 - 8 = 15 [ANSWER]