Question

The heights of a maple tree and a cherry tree have a ratio of 5:2. If the maple tree grew 20 cm and 20 cm was cut off the top of the cherry tree, the ratio of their heights would be 3:1. How much taller is the maple tree than the cherry tree?

Answer 1

Let x be the heights of a maple tree and y be the height of the cherry tree.
We know: 
$\frac{x}{y} = \frac{5}{2}$
The new ratio is obtained like this:
$\frac{x+20}{y-20} = \frac{3}{1}$.
From the above equation we get $x= (y-20)\frac{3}{1} -20$.
then $\frac{ (y-20)\frac{3}{1} -20}{y} = \frac{5}{2}$
Solving the above equation for y we get: $y=160$
So $x=400$
So the first tree is (400-160=240) more taller than cherry tree.