Question

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.

Answer 1

Let the cost price of saree be Rs. $x$ and the list price of sweater be Rs. $y$.
Situation 1: By selling a saree at 8 % profit and a sweater at 10 % discount, the shopkeeper gets Rs. 1008.
$\Rightarrow \frac{108x}{100}+\frac{90y}{100}=1008$

$\Rightarrow 54x+45y=50400$ ............(1)

Situation 2: By selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.

$\Rightarrow \frac{110x}{100}+\frac{92y}{100}=1028\Rightarrow 55x+46y=51400$ ...........(2)

Now, multiplying the equation (1) by 55 and (2) by 54, we get.
2970x + 2475y = 2772000 ............(3)
and 2970x + 2484y = 2775600 .............(4)

Now, subtracting (3) from (4), we get
9y = 3600
$\Rightarrow$ y = 400

Hence, x = 600

So, the cost price of a saree is Rs. 600 and the list price of a sweater is Rs. 400.