A shopkeeper sells a saree at 8% profit and a sweater at 10%discount earn ₹1008.If she sells saree at 10%profit and the sweater at 8%discount earns ₹1028.Find the cost price of saree and list price of sweater.
Answers
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 = 3600y = 3600/9y = 400Putting the value of y = 400 in (1). , we get.54x + 45y = 5040054x + (45*400) = 5040054x + 18000 = 5040054x = 50400 - 1800054x = 32400x = 32400/54x = 600. So, the cost price of a saree is Rs. 600. and the list price of a sweater is Rs. 400 I hope it helps u
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