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

Question

Philoid · Accepted Answer

Let the cost price of the saree and the list price of the sweater be ₹ x and ₹ y, respectively.

Case I Sells a saree at 8% profit + Sells a sweater at 10% discount = ₹ 1008

…(i)

Case II Sold the saree at 10% profit + Sold the sweater at 8% discount = ₹ 1028

(100 + 10)% of x + (100-8%) of y = 1028
110% of x + 92% of y = 1028
1.10x + 0.92 y = 1028 …(ii)

On putting the value of y from Eq. (i) into Eq. (ii), we get

1.1 × 0.9x + 0.92 × (1008-1.08x) = 1028×0.9
0.99x-0.9936x = 9252-927.36
-0.0036x = -2.16

On putting the value of x in Eq. (i), we get

Hence, the cost price of the saree and the list price (price before discount) of the sweater are ₹ 600 and ₹ 400, respectively.