Litmus paper is an indicator that identifies if a substance is basic or acidic. Red litmus paper turns blue in basic solution and remains unaffected in acidic solution. Blue litmus paper turns red in acidic solution and remains unaffected in basic solution.
Metal oxides are generally basic in nature. Rust is hydrated iron oxide. It is formed when iron reacts with oxygen and moisture. Therefore, rust is basic in nature. So the colour of red litmus paper will turn blue and the colour of blue litmus paper will remain unaffected when they are dipped in a suspension of rust and water.