A false balance has equal arms. An object weighs ${\mathrm{W}}_1$ when placed in one pan and ${\mathrm{W}}_2$ when placed in the other pan. The true weight W of the object is

Let true weight of the object is W and weight of right pan is x more than left pan.

Now suppose the object is placed in left pan:

W = ${\mathrm{W}}_1 + \mathrm{x}$  ------(1)

Now if the object is placed in right pan.

${\mathrm{W}}_2 = \mathrm{W}+\mathrm{x}$--------(2)

from (1) and (2)    W = $\frac{{\mathrm{W}}_1+{\mathrm{W}}_2}{2}$