A shopkeeper sells a sari at …

Let the cost price of a saree be Rs. x and the list price of a sweater be Rs. y.
We know that, Selling Price is given by :-{tex}S\cdot P\cdot=C\cdot P\cdot\left(1+\frac{profit\;percentage}{100}\right){/tex}
{tex}\Rightarrow{/tex} S.P. of saree at 8% profit = {tex}x(1+\frac8{100}){/tex}

{tex}= \left( {x + \frac{{8x}}{{100}}} \right) = \left( {\frac{{108x}}{{100}}} \right){/tex}

Also, Selling Price is given by :-

{tex}S.P.\;=\;L.P.(1-\frac{discount\;percentage}{100}){/tex}
{tex}\Rightarrow{/tex} S.P. of sweater at 10% discount {tex} = \left( {y - \frac{{10y}}{{100}}} \right) = \left( {\frac{{90y}}{{100}}} \right){/tex}
According to question,
{tex}\frac{{108x}}{{100}} + \frac{{90y}}{{100}} = 1008{/tex}
{tex}\Rightarrow{/tex} 108x + 90y = 100800 ...(i)
Now, S.P. of saree at 10% profit {tex}= \left( {x + \frac{{10x}}{{100}}} \right) = \left( {\frac{{110x}}{{100}}} \right){/tex}
S.P. of sweater at 8% discount {tex} = \left( {y - \frac{{8y}}{{100}}} \right) = \left( {\frac{{92y}}{{100}}} \right){/tex}
According to question,
{tex}\frac{{110x}}{{100}} + \frac{{92y}}{{100}} = 1028{/tex}
{tex}\Rightarrow{/tex} 110x + 92y = 102800 ...(ii)
Subtracting equation (i) from equation (ii), we get ;
(110x + 92y) -(108x + 90y)=102800 -100800.
{tex}\Rightarrow{/tex}2x + 2y = 2000
{tex}\Rightarrow{/tex} x + y = 1000
{tex}\Rightarrow{/tex} x = 1000 - y ...(iii)
Substituting x = 1000 - y from equation (iii) in equation (i), we get
108(1000 - y) + 90y = 100800
{tex}\Rightarrow{/tex} 108000 - 108y + 90y = 100800
{tex}\Rightarrow{/tex} -18y = -7200
{tex}\Rightarrow{/tex} y = 400
Putting value of y in equation (iii) 
{tex}\Rightarrow{/tex} x = 1000 - 400 = 600
Thus, the cost price of saree is x = Rs.600
and the list price of sweater is y = Rs.400.