Solution :-

Let the cost price of saree be Rs. 'x' and the list price of sweater be Rs. y.

Therefore,

Situation 1 -

By selling a saree at 8 % profit and a sweater at 10 % discount, the shopkeeper gets Rs. 1008

⇒ 108x/100 + 90y/100 = 1008

⇒ 27x/25 + 9y/10 = 1008/1

Taking L.C.M. of the denominators and then solving it, we get.

54x + 45y = 50400 ............(1)

Situation 2 -

by selling a saree at 10 % profit and a sweater at 8 % discount, the shopkeeper gets Rs. 1028.

⇒ 110x/100 + 92y/100 = 1028

⇒ 11x/10 + 23y/25 = 1028/1

Taking L.C.M. of the denominators and then solving it, we get.

⇒ 55x + 46y = 51400 ...........(2)

Now, multiplying the equation (1) by 55 and (2) by 54, we get.

(54x + 45y = 50400)*55

= 2970x + 2475y = 2772000 ............(3)

(55x + 46y = 51400)*54

= 2970x + 2484y = 2775600 .............(4)

Now, subtracting (3) from (4), we get.

2970x + 2484y = 2775600 2970x + 2475y = 2772000 - - - ___________________________

9y = 3600___________________________

⇒ 9y = 3600

y = 3600/9

y = 400

Putting the value of y = 400 in (1), we get.

54x + 45y = 50400

54x + (45*400) = 50400

54x + 18000 = 50400

54x = 50400 - 18000

54x = 32400

x = 32400/54

x = 600

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