divide 34 into two parts in such a way 4/7th of one part is equal to 2/5thof the other part

We are given that 34 is divided in to two parts. So, let the first part be x and second part be 36 - x.

According to question,

$$\begin{gathered} \frac{4x}{7} = \frac{2}{5}\left(34 - x\right) \\ \mathrm{cross} \mathrm{multiplying} \mathrm{the} \mathrm{denominators}, \mathrm{we} \mathrm{get} \\ \Rightarrow 20x = 14 (34 - x) \\ \Rightarrow 20x = 476 - 14x \\ \Rightarrow 20x + 14x = 476 \\ \Rightarrow 34x = 476 \\ \Rightarrow x = \frac{476}{34} = 14 \end{gathered}$$

Now, we have got the first part, that is, x = 14.

Thus, another part = $\frac{2}{5}\left(34 - x\right) = \frac{2}{5}\left(34 - 14\right) = \frac{2}{5} \times 20 = 8$

Hope it helps you!