If you travelling through a proper travel sources like mumbai local . Then you dont need to worry because in mumbai locals, the girls/ladies compartment are separated from remag compartment. The Maharashtra gov had done this by keeping in mind about the safety of girls//ladies. Still here i am giving you some safety travelling tips:
Keep your travel plans, including accommodation details, to yourself.
Don't hitch hike.
Try not to travel at night.
Avoid 'seedier' areas of the cities you visit, especially at night.
Ask your hotel manager for advice on 'safe' versus 'unsafe' local areas.
As a general rule, city streets that include children and women suggest the area is safe for families.
Keep a photocopy of your passport and all other important documents in a safe place.
Use ATMs during the day, when there are people around.
Try to rely more on credit cards and travellers cheques than cash.
If you are mugged, don't fight back. It is better to lose a few dollars and a wristwatch than get injured.
Avoid incidents such as fights, riots or civil disturbances at all times.