Question

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.

Answer 1

Let the cost price of the saree and the list price of the sweater be Rs. `x` and Rs. Y, respectively.
Case I Sells a saree at 8% profit + Sells a Sweater at 10%( discount = Rs. 1008
`rArr " " (100+8)%` of `x+(100-10)%`of `y=1008`
`rArr " "` 108% of x +90% of y= 1008
`rArr " " 1.08x+0.9y=1008 " " ...(i)`
Case II Sold the saree at 10% profit + Sold the sweater at 8% discount = Rs. 1028
`rArr " " `(100+10)%of x+(100-8)% of y=1028
`rArr " " `110%of x + 92% of y = 1028
`rArr " " 1.1x+0.92y=1028 " " ...(ii)`
On putting the value of y from Eq. (i) into Eq. (ii), we get
`1.1x+0.92((1008-1.08x)/(0.9))=1028`
`rArr " " 1.1xx0.9x+927.36-0.9936x=1028xx0.9`
`rArr " " 0.99x-0.9936x=9252-927.36`
`rArr " " -0.0036x=-2.16`
`:. " " x(2.16)/(0.0036)=600`
On putting the value of x in Eq. (i) , we get
`1.08xx600+0.9y=1008`
`rArr " " 108xx6+0.9y=1008`
`rArr " " 0.9y=1008-648`
`rArr " " 0.9y=360`
`rArr " " y=(360)/(0.9)=400`
Hence, the cost price of the saree and the list price (price before discount) of the sweater are Rs. 600 and Rs. 400, respectively.