A 10km long underground cable extends from east to west and consists of two parallel wires, each of which has resistance $=13\mathrm{\Omega }/\mathrm{km}$ . A short develops at distance x from the west end when a conducting path of resistance R connects the wires. The resistance of the wires and the short is then $100\mathrm{\Omega }$  when measurement is made from east end, and $200\mathrm{\Omega }$  when it is made from the west end. What is the value of R (ohm)?