Question

divide 120 into two parts such that 2/3 of one part is equal to 2/5 of the other part.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{one}\mathrm{part}=\mathrm{x} \\ \mathrm{So},\mathrm{other}\mathrm{part}=120-\mathrm{x} \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \frac{2}{3}\mathrm{x}=\frac{2}{5}\times \left(120-\mathrm{x}\right) \\ \Rightarrow \frac{2\mathrm{x}}{3}=\frac{2\left(120-\mathrm{x}\right)}{5} \\ \Rightarrow 10\mathrm{x}=6\left(120-\mathrm{x}\right) \\ \Rightarrow 10\mathrm{x}=720-6\mathrm{x} \\ \Rightarrow 10\mathrm{x}+6\mathrm{x}=720 \\ \Rightarrow 16\mathrm{x}=720 \\ \Rightarrow \mathrm{x}=\frac{720}{16} \\ \Rightarrow \mathrm{x}=45 \\ \mathrm{Thus},\mathrm{the}\mathrm{two}\mathrm{part}\mathrm{will}\mathrm{be}45\mathrm{and}120-45=75 \end{gathered}$$