Sol:

Let Cost Price (CP) of saree Rs x

Let Cost Price (CP) of sweater Rs y

According to the first condition given in the question:

A shopkeeper sells a saree at 8% profit and a sweater at a 10% discount.

Therefore,

The selling price (SP) of the saree is

$\Rightarrow Rs. x + \frac{8x}{100}$ $\Rightarrow \frac{108}{100} —[1]$

The selling price (SP) of the sweater is

$\Rightarrow Rs. y – \frac{10y}{100}$ $\Rightarrow \frac{90y}{100} —[2]$

Now by adding both the equations – [1] and [2], we get

$\Rightarrow \frac{108x}{100} + \frac{90y}{100} = 1008 —[3]$

According to the second condition given in the question:

A shopkeeper sells a saree at 10% profit and a sweater at 8% discount,

Therefore,

The selling price (SP) of the saree is

$\Rightarrow Rs. x + \frac{10x}{100}$ $\Rightarrow \frac{110x}{100}$

The selling price (SP) of the sweater is

$\Rightarrow Rs. y – \frac{8y}{100}$ $\Rightarrow \frac{92y}{100}$

Now by adding both the equations – [4] and [5], we get

$\Rightarrow \frac{110x}{100} + \frac{92y}{100} = 1028—[4]$

Now by solving both the equations – [3] and [4], we get

$\Rightarrow 108x + 90y = 100800 —[5]$ $\Rightarrow 110x + 92y = 102800—[6]$

Now by subtracting both the equations – [5] and [6], we get

$\Rightarrow 2x + 2y = 2000$ $\Rightarrow x + y = 1000—[7]$

Now by substituting the value of equation (7) in equation (5), we get

$\Rightarrow 108x + 90y$ $\Rightarrow 108x + 90 (1000 – x) = 100800$ $\Rightarrow 108x – 90x = 100800 – 90000$ $\Rightarrow 18x = 10800$ $\Rightarrow x = 600$

Therefore, the cost of the saree is Rs 600

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