2 men and 1 woman together can complete a piece of work in 14 days. 4 women and 2 men together can do it in 8 days. If a man gets ₹600 per day, how much should a woman get per day?

Let the efficiency of a man be $M$ and a woman be $W$.
According to the question, total work is equal in both cases:

$$(2M+1W)\times 14=(2M+4W)\times 8$$

$$28M+14W=16M+32W$$

$$28M-16M=32W-14W$$

$$12M=18W$$

$$\frac{M}{W}=\frac{18}{12}=\frac{3}{2}$$

The ratio of daily wages is equal to the ratio of their daily work efficiency.

$$\frac{\text{Wages of Man}}{\text{Wages of Woman}}=\frac{3}{2}$$

Given that a man gets ₹600 per day:

$$\frac{600}{\text{Wages of Woman}}=\frac{3}{2}$$

$$\text{Wages of Woman}=\frac{600\times 2}{3}=400$$

A woman should get ₹400 per day.