We know thatFinal price \\\\(=\\\\) initial price\\\\({ \\left( 1+\\frac { rate }{ 100 } \\right) }^{ time }\\\\)Here the final price \\\\(=\\\\) Rs. \\\\(8784\\\\), time \\\\(=3\\\\) yrs, rate \\\\(=-10\\% \\\\)p.a.The rate is negative since the price is depriciating.Let the initial price \\\\(=\\\\) Rs. \\\\(x\\\\).\\\\(\ herefore x\ imes { \\left( 1-\\dfrac { 10 }{ 100 } \\right) }^{ 3 }=8748\\\\)\\\\( \\Rightarrow x\ imes \\dfrac { 9 }{ 10 } \ imes \\dfrac { 9 }{ 10 } \ imes \\dfrac { 9 }{ 10 } =8748\\\\)\\\\( \\Rightarrow x=8748\ imes \\dfrac { 10 }{ 9 } \ imes \\dfrac { 10 }{ 9 } \ imes \\dfrac { 10 }{ 9 } =\\\\) Rs. \\\\(12000\\\\)So, the price of the machine \\\\(3\\\\) years back \\\\(=\\\\) Rs. \\\\(12000\\\\).Ans- Option C.