The scheme to reduce the interest burden of the State Government in India through the gradual conversion of high-cost debt into low-cost debt is known as the debt-swap scheme. This scheme is aimed at helping the State Government to manage their debt more effectively and decrease their interest expenses.

Option 1: Debt-swap scheme - This is the correct answer. It refers to the scheme that allows the State Government to swap their high-cost debt with low-cost debt, thereby reducing their interest burden.

Option 2: Debt-write-off scheme - This option is incorrect. Debt-write-off refers to canceling or forgiving a debt, which is not the same as converting it into low-cost debt.

Option 3: Grants-in-aid scheme - This option is incorrect. Grants-in-aid scheme involves providing financial assistance to the State Government, but it does not involve the conversion of high-cost debt into low-cost debt.

Option 4: Debt consolidation scheme - This option is incorrect. Debt consolidation scheme involves combining multiple debts into a single debt, but it does not necessarily involve converting high-cost debt into low-cost debt.

In conclusion, the correct answer is option 1, the debt-swap scheme, which helps the State Government reduce their interest burden by converting high-cost debt into low-cost debt