<?xml version='1.0' encoding='UTF-8'?>
<FilingSummary>
  <Version>3.3.0.814</Version>
  <ProcessingTime/>
  <ReportFormat>html</ReportFormat>
  <ContextCount>25</ContextCount>
  <ElementCount>99</ElementCount>
  <EntityCount>1</EntityCount>
  <FootnotesReported>false</FootnotesReported>
  <SegmentCount>9</SegmentCount>
  <ScenarioCount>0</ScenarioCount>
  <TuplesReported>false</TuplesReported>
  <UnitCount>8</UnitCount>
  <MyReports>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R1.htm</HtmlFileName>
      <LongName>101 - Document - Document and Entity Information</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DocumentandEntityInformation</Role>
      <ShortName>Document and Entity Information</ShortName>
      <MenuCategory>Cover</MenuCategory>
      <Position>1</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R2.htm</HtmlFileName>
      <LongName>103 - Statement - Balance Sheets</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/StatementOfFinancialPositionClassified</Role>
      <ShortName>Balance Sheets</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>2</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R3.htm</HtmlFileName>
      <LongName>104 - Statement - Balance Sheets (Parenthetical)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/StatementOfFinancialPositionClassifiedParenthetical</Role>
      <ShortName>Balance Sheets (Parenthetical)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>3</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R4.htm</HtmlFileName>
      <LongName>105 - Statement - Statements of Income</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/StatementOfIncomeAlternative</Role>
      <ShortName>Statements of Income</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>4</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R5.htm</HtmlFileName>
      <LongName>106 - Statement - Statements of Cash Flows</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/StatementOfCashFlowsIndirect</Role>
      <ShortName>Statements of Cash Flows</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>5</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R6.htm</HtmlFileName>
      <LongName>107 - Disclosure - Basis of Presentation</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsOrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</Role>
      <ShortName>Basis of Presentation</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>6</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R7.htm</HtmlFileName>
      <LongName>108 - Disclosure - Net Income Per Limited Partnership Unit</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsEarningsPerShareTextBlock</Role>
      <ShortName>Net Income Per Limited Partnership Unit</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>7</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R8.htm</HtmlFileName>
      <LongName>109 - Disclosure - Leasing Activities</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsLeasesOfLessorDisclosureTextBlock</Role>
      <ShortName>Leasing Activities</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>8</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R9.htm</HtmlFileName>
      <LongName>110 - Disclosure - Transactions with Del Taco</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsRelatedPartyTransactionsDisclosureTextBlock</Role>
      <ShortName>Transactions with Del Taco</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>9</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R10.htm</HtmlFileName>
      <LongName>111 - Disclosure - Distributions</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsPartnersCapitalNotesDisclosureTextBlock</Role>
      <ShortName>Distributions</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>10</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R11.htm</HtmlFileName>
      <LongName>112 - Disclosure - Payable to Limited Partners</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsOtherLiabilitiesDisclosureTextBlock</Role>
      <ShortName>Payable to Limited Partners</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>11</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R12.htm</HtmlFileName>
      <LongName>113 - Disclosure - Concentration of Risk</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsConcentrationRiskDisclosureTextBlock</Role>
      <ShortName>Concentration of Risk</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>12</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R13.htm</HtmlFileName>
      <LongName>114 - Disclosure - Purchase and Sale Agreement</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsPurchaseAndSaleAgreementTextBlock</Role>
      <ShortName>Purchase and Sale Agreement</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>13</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R14.htm</HtmlFileName>
      <LongName>115 - Disclosure - Basis of Presentation (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/NotesToFinancialStatementsOrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlockPolicies</Role>
      <ShortName>Basis of Presentation (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <Position>14</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R15.htm</HtmlFileName>
      <LongName>116 - Disclosure - Net Income Per Limited Partnership Unit - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosureNetIncomePerLimitedPartnershipUnitAdditionalInformation</Role>
      <ShortName>Net Income Per Limited Partnership Unit - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>15</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R16.htm</HtmlFileName>
      <LongName>117 - Disclosure - Leasing Activities - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosureLeasingActivitiesAdditionalInformation</Role>
      <ShortName>Leasing Activities - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>16</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R17.htm</HtmlFileName>
      <LongName>118 - Disclosure - Transactions with Del Taco - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosureTransactionsWithDelTacoAdditionalInformation</Role>
      <ShortName>Transactions with Del Taco - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>17</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R18.htm</HtmlFileName>
      <LongName>119 - Disclosure - Distributions - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosureDistributionsAdditionalInformation</Role>
      <ShortName>Distributions - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>18</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R19.htm</HtmlFileName>
      <LongName>120 - Disclosure - Payable to Limited Partners - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosurePayableToLimitedPartnersAdditionalInformation</Role>
      <ShortName>Payable to Limited Partners - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>19</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R20.htm</HtmlFileName>
      <LongName>121 - Disclosure - Concentration of Risk - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosureConcentrationOfRiskAdditionalInformation</Role>
      <ShortName>Concentration of Risk - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>20</Position>
    </Report>
    <Report instance="dtrpi-20150930.xml">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R21.htm</HtmlFileName>
      <LongName>122 - Disclosure - Purchase and Sale Agreement - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://deltaco.com/taxonomy/role/DisclosurePurchaseAndSaleAgreementAdditionalInformation</Role>
      <ShortName>Purchase and Sale Agreement - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>21</Position>
    </Report>
    <Report>
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <LongName>All Reports</LongName>
      <ReportType>Book</ReportType>
      <ShortName>All Reports</ShortName>
    </Report>
  </MyReports>
  <Logs>
    <Log type="Info">In ''Balance Sheets'', column(s) 3, 4 are contained in other reports, so were removed by flow through suppression.</Log>
    <Log type="Info">In ''Statements of Cash Flows'', column(s) 1, 2 are contained in other reports, so were removed by flow through suppression.</Log>
  </Logs>
  <InputFiles>
    <File>dtrpi-20150930.xml</File>
    <File>dtrpi-20150930_cal.xml</File>
    <File>dtrpi-20150930_def.xml</File>
    <File>dtrpi-20150930_lab.xml</File>
    <File>dtrpi-20150930_pre.xml</File>
    <File>dtrpi-20150930.xsd</File>
  </InputFiles>
  <SupplementalFiles/>
  <BaseTaxonomies/>
  <HasPresentationLinkbase>true</HasPresentationLinkbase>
  <HasCalculationLinkbase>true</HasCalculationLinkbase>
</FilingSummary>

