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

230V is much more efficient to run lengths longer lengths.

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 that240V 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.

There is not any big scientific or electrical reason  as to why in US and some other parts of the World use 60Hz and in India and certain other
 parts of the World use 50 Hz.
It is just the way it has been started and it continues so.Changing this system would cost a lot.

Ankit Srivastava, Cricket loverAnswered Apr 6 2015

Image courtesy: Graphs, Infographics

The tussle between Nikola Tesla and Thomas Edison is heard by most of us. It is believed that Edison’s early experiments with the Direct Current (DC) power somewhere in late 1800s showed first mainstream application for electricity, however it suffered from a tendency to lose voltage over long distances. On the other hand Nikola Tesla invented something called Alternating Current (AC) power which can be easily transmitted over long-distance, this was a direct competition to Edison’s Technology and it happened to be 110V. It is also believed that 110V is more economic and during the earlier times electricity was delivered to homes and businesses for the sole purpose of lighting. The other electrical equipment came much later. At that time effective form of a light bulb was a carbon filament bulb that operated best at 100-110V. 
There was a lot of tussle between Edison and Tesla, words were exchanged, Elephants were electrocuted, and eventually it was settled that AC power was the only option. The first company to buy Tesla’s patents for power transmission, Westinghouse Electric (founded by George Westinghouse) settled on an easy standard: 60Hz – 110V. 
Now the frequency of the AC supply depends upon the design and the rotatory speed of the generator. Generators operated by slow speed engines will produce lower frequencies, for a given number of poles, than those operated by for example a high speed steam turbine, these factors plays an important role to decide the operating frequency.
However in Europe, specifically in Germany, BEW exercised their monopoly to push things a little further and they arbitrarily set 50Hz as frequency and increased the voltage up to 240V to improve distribution efficiency. This slowly spread to entire Europe. This standard was adopted by India as well. 
This however led to the world being divided into two frequency standard. Most 60Hz systems are nominally 120V and most 50Hz systems are nominally 230V.

https://www.quora.com/Why-does-India-use-230-V-50HZ-while-the-USA-uses-120V-60HZ