**Question:**

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum ₹ 1008. If she had sold the saree at 10% profit and the

sweater at 8% discount, she would have got ₹ 1028 then find the cost of the saree and the list price (price before discount) Of the sweater.

**Solution:**

Let the cost price of the saree and the list price of the sweater be ₹ x and ₹ y, respectively.

Case I Sells a saree at $8 \%$ profit + Sells a sweater at $10 \%$ discount $=₹ 1008$

$\Rightarrow \quad(100+8) \%$ of $x+(100-10) \%$ of $y=1008$

$\Rightarrow \quad 108 \%$ of $x+90 \%$ of $y=1008$

$\Rightarrow \quad 1.08 x+0.9 y=1008$ $\ldots$ (i)

Case II Sold the saree at $10 \%$ profit + Sold the sweater at $8 \%$ discount $=₹ 1028$

$\Rightarrow \quad(100+10) \%$ of $x+(100-8) \%$ of $y=1028$

$\Rightarrow \quad 110 \%$ of $x+92 \%$ of $y=1028$

$\Rightarrow \quad 1.1 x+0.92 y=1028$ .....(ii)

On putting the value of $y$ from Eq. (i) into Eq. (ii), we get

$1.1 x+0.92\left(\frac{1008-1.08 x}{0.9}\right)=1028$

$\Rightarrow \quad 1.1 \times 0.9 x+927.36-0.9936 x=1028 \times 0.9$

$\Rightarrow \quad 0.99 x-0.9936 x=9252-927.36$

$\Rightarrow \quad-0.0036 x=-2.16$

$\therefore$ $x=\frac{2.16}{0.0036}=600$

On putting the value of $x$ in Eq. (i), we get

$1.08 \times 600+0.9 y=1008$

$\Rightarrow \quad 108 \times 6+0.9 y=1008$

$\Rightarrow \quad 0.9 y=1008-648$

$\Rightarrow \quad 0.9 y=360$

$\Rightarrow \quad y=\frac{360}{0.9}=400$

Hence, the cost price of the saree and the list price (price before discount) of the sweater are ₹ 600 and ₹ 400, respectively.