It is desired to extract fuel from a solid raw material with a suitable solvent. Fuel is extracted from the solid containing $20\%$fuel and $80\%$ clay with a suitable solvent $($S$).$ The concentrated solution $($upper stream$)$ obtained contains $40\%$ fuel and $60\%$ solvent $($S$).$ The underflows leaving each stage contain $30\%$ solution and $70\%$ clay. The bottom stream leaving the extraction system contains $5\%$ fuel and $72\%$ clay. Find the required number of stages.