correct answer is: ₹\;1400\;\&\;₹\;2500

Explanation

Here, given ratio \large\frac25\;:\;\frac57
And total amount ₹\;3900.
Let,
A’s amount ₹\;\large\left(\frac{2}{5}\normalsize\times x\right)\normalsize=\large\frac{2x}{5}
B’s amount ₹\;\large\left(\frac{5}{7}\normalsize\times x\right)\normalsize=\large\frac{5x}{7}
According to the question,
\large\left(\frac{2x}{5}+\frac{5x}{7}\right)\normalsize=₹\;3900
\rightarrow\large\left(\frac{14x+25x}{35}\right)\normalsize=3900 _{[LCM 35]}
\rightarrow\large\frac{39x}{35}\normalsize=3900
\rightarrow 39x=\left(3900\times35\right)
\rightarrow x=\large\frac{\left(3900\times35\right)}{39}
\rightarrow x=3500
So that, A’s amount ₹\;\large\frac{2x}{5}\normalsize=\large\frac{2\times3500}{5}\normalsize=1400.
And, B’s amount ₹\;\frac{5x}{7}\normalsize=\large\frac{5\times3500}{7}\normalsize=2500.
Ans: A gets ₹\;1400 and B gets ₹\;2500.

Alternative phrasings for this particular query are:

1. Divide ₹ 3900 between A and B in the ratio of 2/5 : 5/7.
2. Distribute ₹ 3900 among A and B such that the ratio of their shares is 2/5 : 5/7.
3. Split ₹ 3900 into two parts for A and B, maintaining the ratio of 2/5 : 5/7.