d
If side of object square \(=\ell\)

and side of image square \(=\ell^{\prime}\)

From question, \(\frac{\ell^{\prime 2}}{{\ell}^2  }=9\)

or \(\quad \frac{\ell^{\prime}}{\ell}=3\)

i.e., magnificationm \(=3\)

\(\mathrm{u}=-40 \mathrm{cm}\)

\(\mathrm{v}=3 \times 40=120\, \mathrm{cm}\)

\(f=?\)

From formula, \(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

\(\frac{1}{120}-\frac{1}{-40}=\frac{1}{f}\)

or, \(\frac{1}{f}=\frac{1}{120}+\frac{1}{40}=\frac{1+3}{120} \therefore f=30\, \mathrm{cm}\)