If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be:

Explanation:-

Here, we use work equivalence method;
10*12 = 12*x;
Or, x = 10 days;

To understand the work equivalence method, we use a graphic as follows:

Men   Days
10 ↓    12
12     ↑ x (let)
Here, the two arrows, downward (↓) and upward (↑) show variation between men and days.
[If downward arrows show decrements then upward arrows show increments and vice-verse.]
Thus,
$$\eqalign{ & \frac{{10}}{{12}} = \frac{{\text{x}}}{{12}} \cr & {\text{or, x}} = \frac{{10 \times 12}}{{12}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 10\,{\text{days}} \cr}$$