Place of supply

SGST is applicable in this transaction. why because

The government will collect CGST, SGST or IGST depending on whether the transaction is Intra-State or Inter-State. When the supply of goods or services happens within a state called as intra-state transactions, then both the CGST and SGST will be collected. Whereas if the supply of goods or services happens between the states called as inter-state transactions and IGST will be collected.

It is to be noted that the GST is a destination based tax, which is received by a State in which the goods are consumed but not by a state in which such goods are manufactured.

 

If bill to and ship to party are same, then can we take it as per section 10(1)(b) supply?

IGST Applicable in Both the cases.

In First Transaction : B to A , Section 10(1)(a) is applicable " Movement of goods by the Supplier or the RECIPIENT" , here in your case the delivery has been taken in Gujrat by Recipient "A" of Rajasthan & in term of clause (e) of rule 46 of CGST Act Tax Invoice issued shall contain, name, & Address of Recipient with State & State Code , so as soon as the state mentioned on bill by supplier B as Rajasthan the IGST need to be charged.
2nd Transaction : A to C
Section 10(1)(a) is applicable " Movement of goods by the SUPPLIER or the recipient" , here in this case the movement of goods is caused by SUPPLIER "A" from Rajasthan & as above in term of Section 46 IGST will be applicable.

"Bill to Ship to " model in term of Section 10(1)(b) can Applicable .

"B" will raise bill in following manner

"B" Gujarat will , Bill to "A" & Ship to "C" , IGST will be applicable.

 

"A" will raise the bill : 

"A"  in Rajasthan will Bill to "C" in Gujarat & Despatch from Gujarat "B" IGST will Applicable.

Above in both the manner the IGST is applicable.

If in this case A mentioned ship to self in the address of gujrat, then what should happen?

even then IGST is Applicable as its being billed to "a" in rajasthan

is "A" is having registered office in Gujrat