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% of female doctors = 26.8%
No. of female doctors = 57,500
We have to find total number of registered doctors.
[tex]\tt\:\%_{Female\;doctors}=\dfrac{No.\;of\;femal\;doctors}{No.\;of\;total\;doctors}\times 100[/tex]
[tex]\leadsto\tt\:\%_{FD}=\dfrac{N_{FD}}{N_{TD}}\times 100[/tex]
[tex]\leadsto\tt\:26.8=\dfrac{57500}{N_{TD}}\times 100[/tex]
[tex]\leadsto\tt\:\dfrac{57500}{N_{TD}}=\dfrac{26.8}{100}[/tex]
[tex]\leadsto\tt\:\dfrac{57500}{N_{TD}}=0.268[/tex]
[tex]\leadsto\tt\:N_{TD}=\dfrac{57500}{0.268}[/tex]
[tex]\leadsto\:\boxed{\bf{N_{TD}\approx 214552}}[/tex]
∴ The total number of registered doctors ≈ 2,14,552