The correct option is A 71.25 cm and 41.25 cm
Let us suppose Lo1 and Lo2 is the length of rod of steel and brass at 0∘C respectively and ΔT change in temperature.
We know, L=Lo(1+αΔT) [linear expansion]
For steel,
L1=Lo1(1+11×10−6ΔT) [αsteel=11×10−6/∘C,given]
=Lo1+11×10−6×ΔT×Lo1...(1)
For brass,
L2=Lo2(1+19×10−6ΔT) [αbrass=19×10−6/∘C,given]
=Lo2+19×10−6×ΔT×Lo2...(2)
On subtracting (1) from (2)
L2−L1=Lo2−Lo1+19×10−6×ΔT×Lo2−11×10−6×ΔT×Lo1
⇒Lo1=19×10−611×10−6Lo2
[L2−L1=Lo2−Lo1 as difference in length is constant, given]
⇒Lo1=1911Lo2 ... (3)
Also, Lo1−Lo2=30 cm [Given]
⇒1911Lo2−Lo2=30 [from (3)]
⇒811Lo2=30
⇒Lo2=41.25 cm ... (4)
On putting (4) in (3),
Lo1=71.25 cm
∴ Lengths of the rods at 0∘ C are 71.25 cm and 41.25 cm of steel and brass respectively.