A shopkeeper sells a saree at8%profit …

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