Why 50 hertz frequency in India ?

IT STARTS FROM THE BEGINNING OF ELECTRICITY-

Early in the history or electricity, Thomas Edison's General Electric 
company was distributing DC electricity at 110 volts in the United States. 
Then Nikola Tesla devised a system of three-phase AC electricity at  240 volts. Three-phase meant that three alternating currents slightly out of phase were combined in order to even out the great variations in voltage occurring in AC electricity. He had calculated that 60 cycles per second or 60Hz was the most effective frequency. 
Tesla later compromised to reduce the voltage to 120 volts for safety reasons.
With the backing of the Westinghouse Company, Tesla's AC system 
became the standard in the United States. 
Westinghouse chose 60 Hz because the arc light carbons(arc lamp) that were popular at that time worked better at 60 Hz than at 50 Hz.

Europe goes to 50Hz and 230V

Meanwhile, the German company AEG started generating electricity and became a virtual monopoly in Europe. 
They decided to use 50Hz instead of 60Hz to better fit their metric standards, but they stayed with 120V.

Europe stayed at 120V AC until the 1950s, just after World War II. 
They then switched over to 220V for better efficiency in 
electrical transmission. Great Britain not only switched to 220V, but 
they also changed from 60Hz to 50Hz to follow the European lead. 
Since many people did not yet have electrical appliances in Europe after the 
war, the change-over was not that expensive for them. 

U.S. stays at 120V, 60Hz

The United States also considered converting to 220V for home use but felt it would be too costly, due to all the 120V electrical appliances people had. 
A compromise was made in the U.S. in that 240V would come into the house where it would be split to 120V to power most appliances. 
Certain household appliances such as the electric stove and electric clothes dryer would be powered at 240V.

India got 50Hz, because it was colonized by England, which when they developed their electrical systems, choose 50 Hz.
From technical point of view operating 50 Hz versus 60 Hz would not make much difference but, to achieve it, either the prime movers - for example steam turbines, gas turbines and diesel engines  would need to be able to tolerate a 20% increase in speed or the alternators they drive - which produce the electricity  would need to be completely rebuilt with extra poles and windings so that they could continue to run at the same rotational speed. 
The costs of doing such re-engineering would be enormous and could not be justified as "economically worthwhile" from the point of view of actual necessity.

We  could have chosen any other frequency other than 50/60 hz but
50/60 HZ is an optimum frequency which keeps the transmission losses to tolerable limits. 
The higher will be the frequency, the more will be the losses.
and lower frequencies would causes the size, weight & hence the cost to increase. Also, more flickers are noticed in lesser frequencies than higher frequencies.

The voltage and frequency of AC electricity varies from country to country throughout the world.
 Most use 220V and 50Hz. About 20% of the countries use 110V and/or 60Hz to power their homes.220V and 60Hz are the most efficient values, but only a few countries use that combination.