All 30 students in a class study at least 1 of the 2 subjects history or Geography .Twice as many study History as Geography .By drawing a Venn diagram or otherwise , find the number of students who study both History and Geography.

Answer 1

If x is the number who study both, then
h + g - x = 30
h = 2g, so
2g + g - x = 30
3g = x+30
This has four possible solutions:
g=11, h=22, 3 study both
g=12, h=24, 6 study both
g=13, h=26, 9 study both
g=14, h=28, 12 study both