Question

What number must be added to each term of the ratio 7:5, so that the ratio becomes 5:4?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{number}\mathrm{to}\mathrm{be}\mathrm{added}\mathrm{be}\mathrm{x}. \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{7+\mathrm{x}}{5+\mathrm{x}}=\frac{5}{4} \\ \Rightarrow 5\left(5+\mathrm{x}\right)=4\left(7+\mathrm{x}\right) \\ \Rightarrow 25+5\mathrm{x}=28+4\mathrm{x} \\ \Rightarrow 5\mathrm{x}-4\mathrm{x}=28-25 \\ \Rightarrow \mathrm{x}=3 \\ \mathrm{So},\mathrm{required}\mathrm{number}=3 \end{gathered}$$