Let R1, R2, H, Q represent numbers of Re1, Rs 2, 50p, 25p coins. Assuming there is a coin for 1 rupee (Re1) and a separate coin for 2 rupees (Rs2), R1+R2+H+Q=58; R1+2R2+0.50H+0.25Q=80/75=80.75 (for convenience). R1=5Q. R2=2R1=10Q=3H. H=10Q/3
5Q+10Q+H+Q=58; 16Q+H=58=16Q+10Q/3; 58Q/3=58, so Q=3. 2R1=10Q=30, so R1=15. R2=2R1=30. H=10Q/3=10. Therefore we have R1=15, R2=30, H=10 and Q=3.
CHECK: Add up the numbers of coins: 15+30+10+3=58 OK. Add up value: 15+60+5+0.75=80.75=Rs80/75.