Step 1: Split the budget into a revenue account and a capital account.
Instead of adding every non-borrowing item at once, work out the gap on the revenue side and the gap on the capital side separately, then add the two gaps.
Step 2: Find the revenue account gap.
$$ \text{Revenue Deficit} = \text{Revenue Expenditure} - \text{Revenue Receipt} = 3{,}75{,}582 - 2{,}65{,}279 = 1{,}10{,}303 $$
Step 3: Find the capital account gap, leaving out public debt items.
Capital side spending (excluding debt repayment) is Capital expenditure plus Disbursement of loans and advances: $$ 31{,}295 + 38{,}614 = 69{,}909 $$ Capital side receipts (excluding fresh borrowing) is Non-debt capital receipt plus Recovery of loans and advances: $$ 3{,}646 + 20{,}733 = 24{,}379 $$ So the capital account gap is $$ 69{,}909 - 24{,}379 = 45{,}530 $$
Step 4: Add the two gaps to get the fiscal deficit.
$$ \text{Fiscal Deficit} = 1{,}10{,}303 + 45{,}530 = 1{,}55{,}833 \ \text{crore} $$ This matches the direct calculation and confirms the government must borrow Rs. 1,55,833 crore to cover this year's gap.
$$ \boxed{1{,}55{,}833} $$