Question

What should be added to each term of the ratio 7 : 13 so that the ratio becomes 2 : 3

Answer 1

Let the numbers that must be added to the ratio 7 : 13 be 'x'.
So, $\frac{7+x}{13+x}=\frac{2}{3}$
After cross-multiplication, we get
3(7 + x) = 2(13 + x)
21 + 3x = 26 + 2x
3x - 2x = 26 - 21
x = 5
Thus, 5 must be added to each term to make the ratio = 2 : 3.