We have to turn the key on in rapid succession several times before the stater will engage

Skoda Rapid has been on sale since November 2011 in the Indian market and has tasted moderate success, despite the presence of several heavyweights like Honda City, Hyundai Verna and Volkswagen Vento in the same segment. With time progressing, the sales of the sedan started deteriorating as its rivals were far more advanced, up-market and affluent. It is what propelled Skoda India to introduce Skoda Rapid Facelift, which comes with several cosmetic upgrades and a subtle bump in power output.
Here are some key points:
What I like:

• Impressive Build quality.
• Driving Dynamics.
• Looks better than outgoing version

What I don't like:

• Precarious after-sales service.
• Maintenance cost is high

Starter selonoid is sticking open.

Replace the ignition switch.You can replace the key tumbler ignition.It mostly is faulty and giving u this problem.

That symptom usually means the solenoid on the starter is bad and no longer is completing the circuit to engage the starter. A new starter will likely solve that issue. A series of rapid clicks would indicate a week battery. You can try repeatedly turning the key to the start position rapidly, sometimes the starter wil start working. You can also try tapping the starter while somebody holds the key in the start position, if the starter engages place it.

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9 times out of 10 it's the realy but check if stater is getting power to crank wire

TAKE THE BATTERY OFF THE ONE SIDE OF THE SELINOID POSTIVE ONE COMMING FROM THE BATTERY KEY ON AND TOUCH IT TOO THE OTHER SIDE OF THE SELINOID WHERE THE CABLE GOES DOWN TO THE STARTER IF THE STARTER ENGAGES WITHOUT THE SENOID SO JUST A COUPLE OF SECONDS DO THIS STATER ENGAGES SELINOID BAD IF THE STATER DON'T ENGAGE THE STARTER IS BAD

There is a poor contact on the wire terminals on your ignition switch, have that changed. Check also stater solenoid.

2 possible things, 1. the contacts in the solinoid on the starter are bad, it would still test good but wouldnt have enouph power to engage the flywheel, replace starter, or 2. bad flywheel, teeth on flywheel are worn or broken, both require removal of starter, remove starter first inspect flywheel for damage, if none replace starter.

try to get a jump from a friend and see what happens, does the same, faulty starter, may need replacing, try to use small hammer and tap lightly on the starter couple time and have a friend start the car while you tap lightly on it. check ignition switch where you stick the key in. stick the key in the ignition and turn the key back and forth jiggle and wiggle it and see if your igniting will make contact. do it several time to test and see if its the ignition problems, this part is not cheap to replace.

NEED TO REPLACE STARTER.