\(\therefore\)\( u = 12\,\, cm, v = ?\)

\((a)\,\,{{f}}\,\, = \,\,20\,\,cm\,\,\,\,\,\,\because \,\,\frac{1}{v}\,\, - \,\,\frac{1}{u}\,\, = \,\,\,\frac{1}{{{f}}}\,\,\,\,\,\,\,\,\therefore \,\,\frac{1}{v}\,\, - \,\,\frac{1}{{12}}\,\, = \,\,\,\frac{1}{{20}}\)

\( \Rightarrow \,\,\,\frac{1}{v}\,\, = \,\,\frac{1}{{20}}\,\, + \,\,\frac{1}{{12}}\,\,\, = \,\,\frac{{3 + 5}}{{60}}\,\,\, = \,\,\frac{8}{{60}}\,\,\)

\( \Rightarrow \,\,\,v\,\, = \,\,\frac{{60}}{8}\,\, = \,\,7.5\,\,cm\)