circuit-designintegrated-circuitne555schematics
I have designed the schematic diagram of the inner components of the 555 Timer IC for understanding the working of the IC, but not sure if I have designed it correctly or not. 
If it is correct can anyone please help me to understand how the Reset is working on the RS flip-flop.
Modified
Without getting into the specific binary coding of inputs, outputs and states, the abstract state diagram should look something like this. The notation on each edge is Input→Output.
Note that I have defined a third output "Refund" that refunds the coins inserted so far, which is a distinct operation from dispensing change along with a snack if 25 cents have been inserted.
Note that most real vending machines hold the coins that the user has inserted in a separate area until a snack has been dispensed, at which time, they are released into the actual coin box. If a refund is requested instead, the user gets his original coins back.
Yes, you can use a 7474 to divide by two.
BUT the set and reset inputs are active low in the 7474, whereas they are active high in the 4013.
This means that to divide by 2, the set and clear must be pulled up or connected to the rail, not to ground.
One further point, with CMOS, inputs should not be left floating, BAD things can happen. Take all inputs on unused sections of the device to rail or ground, it doesn't matter which, obviously take all used inputs to the correct logic level. Outputs should be left unconnected if not used.
Download a data sheet for both parts and study them carefully for pinout and pin function, IIRC the packages are not pin-compatible, so you will have to change the pin numbers as well.
Best Answer
No, it is not correct.
The reset pin is an active-low additional reset line of the flip flop, as shown before (and on the functional description on the 555 datasheet).
Your schematics must be modified. Here's my suggestions (in red).
Basically, the inverter creates an active high-reset. The OR gate allows to reset the flip flop either due to "threshold" voltage exceeded (CMP2 output high) or due to external reset (low) on pin 4. Basically it creates an additional reset input.