A copper rod of 88 cm and an aluminium rod of unknown length have their difference in length independent of increase in temperature. The length of aluminium rod is $\left({\mathrm{\alpha }}_{\mathrm{Cu}}=1.7\times {10}^{-5}{ \mathrm{K}}^{-1}\text{and }{\mathrm{\alpha }}_{\mathrm{Al}}=2.2\times {10}^{-5}{ \mathrm{K}}^{-1}\right)$

If the increase in length is independent of temperature, then they must have equal expansion. So,
${\ell }_{\mathrm{A}\ell }{\alpha }_{\mathrm{A}\ell }={\ell }_{\mathrm{Cu}}{\alpha }_{\mathrm{CU}}$
$\text{Given}{\ell }_{cu}=88\mathrm{cm}.{\alpha }_{cu}=1.7\times {10}^{-5}{\mathrm{k}}^{-1}$
${\alpha }_{\mathrm{Al}}=2.2\times {10}^{-5}{\mathrm{k}}^{-1}$
$\text{Substituting}{\ell }_{\mathrm{A}\ell }=\frac{{\ell }_{\mathrm{cu}}{\alpha }_{\mathrm{Cu}}}{{\alpha }_{\mathrm{A}\ell }}=\frac{88\times 1.7\times {10}^{-3}}{2.2\times {10}^{-5}}$

$=68\mathrm{cm}\text{.}$