Three rods of identical cross - section and length are made of three different material of thermal conductivity `k_(1) , k_(2)` and `k_(3)` respectively. They are joined together at their ends to make a long rod (See figure). One end of the long rod is maintained at `100^(@)C` and the other at `0^(@)C` ( See figure ). If the joints of the rod are at `70^(@)C` and `20^(@)C` in steady state and there is no loss of energy form the surface of the rod, the correct relationship between `k_(1), k_(2)` and `k_(3)` is

Options

A. `k_(1) : k_(3) = 2 :3 `
` k_(2) : k_(3) = 2 : 5`
B. `k_(1) lt k_(2) lt k_(2) `
`k_(1) : k_(2) = 5 : 2 `
C. `k_(1) : k_(2) = 5 : 2 `
`k_(1) : k_(3) = 3 : 5`
D. `k_(1) gt k_(2) gt k_(3)`