Correct Answer - C
Length of iron rod at `100^@C`
`L_1=50[1+12xx10^-6xx(100-20)]=50.048cm`
Length of aluminum rod at `100^@C`,
`L_2=100[1+24xx10^-6xx(100-20)]=100.192cm`
The length of composite system at `23^@C`
`=50+100=150cm`
and length of composite system at `100^@C`
`=50.048+100.192=150.24cm`
Average`alpha=(0.24cm)/(150cmxx(100-20))`
`=20xx10^(-6)//^@C`
The above shortcut is applicable only if `alpha` varies linearly.