What is the ratio whose terms differ by 40 and the measure of which is $$\frac{2}{7}$$ ?

Solution (By Examveda Team)

Let the terms of the ratio be x and x + 40
$$\eqalign{ & {\text{Then,}} \cr & = \frac{x}{{x + 40}} = \frac{2}{7} \cr & \Rightarrow 7x = 2x + 80 \cr & \Rightarrow 5x = 80 \cr & \Rightarrow x = 16 \cr & \therefore {\text{Required ratio}} \cr & = 16:56 \cr} $$