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

Explanation

Let the cost price of a saree = Rs. X
and the list price of sweater = Rs. Y
Case I :
(S.P. of a saree at 8% profit) + (S.P. of a sweater at 10% discount) - Rs. 1008
`implies ((100+8))/(100)x + ((100-10))/(100)y = 1008`
implies 108x + 90y = 100800
implies 6x + 5y = 5600 ...(1)
Case II :
(S.P. of a saree at 10% profit) + (S.P. of a sweater at 8% discount) = Rs. 1028
`implies ((100+10))/(100) x + ((100 - 8))/(100) y = 1028`
implies 110x + 92y = 102800 ...(2)
Dividing equation (2) by 2, we have
55x + 46y = 51400 ...(3)
Again, multiplying equation (3) by 5, we get
275x + 230y = 257000 ...(4)
Multiplying equation (1) by 46, we get
276x + 230y = 257600 ...(5)
Subtracting equation (5) from (4), we get
`{:(275x + 230y = 257000),(276x + 230y = 257600),(ul("- - -")),(-x = 257000 - 257600):}`
implies -x = - 600
implies x = Rs. 600
Now, 6x + 5y = 5600 [from (1)]
implies `6 xx 600` + 5y = 5600 (`because` x = 600)
implies 5y = 5600 - 3600
implies `y = (2000)/(5)`
implies y = 400
Hence, the C.P. of a saree and C.P. of a sweater are Rs. 600, Rs. 400 respectively.