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Leasing Activities - Additional Information (Detail) (USD $)
12 Months Ended
Dec. 31, 2014
Restaurants
Property
Dec. 31, 2013
Property
Dec. 31, 2012
Property
Operating Leased Assets [Line Items]      
Number of lease years 35 years    
Percentage of gross sales of restaurants 12.00%dtrpi_PercentageOfGrossSalesOfRestaurants    
Leases expiration period 2020 to 2021    
Minimum rentals due per month to Partnership $ 3,500us-gaap_OperatingLeasesRentExpenseMinimumRentals    
Number of properties leased 6us-gaap_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnits 6us-gaap_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnits 6us-gaap_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnits
Number of properties subleased to Del Taco franchisee 1dtrpi_SubleasedAssetsNumberOfUnits    
Number of restaurants operated 5dtrpi_NumberOfRestaurantsOperated    
Combined unaudited sales 5,783,887us-gaap_SalesRevenueGoodsGross 5,500,615us-gaap_SalesRevenueGoodsGross 5,284,393us-gaap_SalesRevenueGoodsGross
Combined unaudited net income (loss) 41,164dtrpi_OperatingLeasesNetIncomeLoss (20,169)dtrpi_OperatingLeasesNetIncomeLoss (22,807)dtrpi_OperatingLeasesNetIncomeLoss
Del Taco franchisee [Member]      
Operating Leased Assets [Line Items]      
Number of restaurants operated 1dtrpi_NumberOfRestaurantsOperated
/ us-gaap_LeaseArrangementTypeAxis
= dtrpi_DelTacoFranchiseeMember
   
Combined unaudited sales $ 930,225us-gaap_SalesRevenueGoodsGross
/ us-gaap_LeaseArrangementTypeAxis
= dtrpi_DelTacoFranchiseeMember
$ 886,332us-gaap_SalesRevenueGoodsGross
/ us-gaap_LeaseArrangementTypeAxis
= dtrpi_DelTacoFranchiseeMember
$ 863,302us-gaap_SalesRevenueGoodsGross
/ us-gaap_LeaseArrangementTypeAxis
= dtrpi_DelTacoFranchiseeMember