In triangle ABC, a line MN is drawn with M on AB and N on AC so that MN is parallel to BC, and AM : MB = 2 : 5. This makes triangle AMN similar to triangle ABC.
Find area(AMN) : area(trapezium MBCN).

AM : AB = 2 : $(2+5)=2$ : 7, so area(AMN) : area(ABC) = ${\left(\frac{2}{7}\right)}^2=\frac{4}{49}$. Taking area(ABC) as 49 parts, triangle AMN is 4 parts and trapezium MBCN is $49-4=45$ parts, giving 4 : 45. The option 4 : 49 compares AMN with the WHOLE triangle instead of with the trapezium, 4 : 25 uses AM : MB by mistake, and 2 : 5 never squares at all.