Question

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

Answer 1

Let the CP of saree be ₹x and the list price of sweater be ₹y.
Case I: When saree is sold at 8% profit and sweater at 10% discount.
SP = CP + Profit
⇒ SP of saree = x + $\frac{8}{100}x$ = $\frac{108}{100}x$
SP of sweater = List price − Discount
⇒ SP of sweater = $y-\frac{10}{100}y$ = $\frac{90}{100}y$
Total sum received by the shopkeeper = ₹1008
⇒ $\frac{108}{100}x$ + $\frac{90}{100}y$ = 1008
⇒ 108x + 90y = 100800
⇒ 6x + 5y = 5600 .....(i)
Case II: When saree is sold at 10% profit and sweater at 8% discount.
⇒ SP of saree = x + $\frac{10}{100}x$ = $\frac{110}{100}x$
SP of sweater = List price − Discount
⇒ SP of sweater = $y-\frac{8}{100}y$ = $\frac{92}{100}y$
Total sum received by the shopkeeper = ₹1028
⇒ $\frac{110}{100}x$ + $\frac{92}{100}y$ = 1028
⇒ 110x + 92y = 102800 .....(ii)
Multiplying (i) by 110 and (ii) by 6, we get
660x + 550y = 616000 .....(iii)
660x + 552y = 616800 .....(iv)
Subtracting (iii) from (iv), we get
2y = 800
⇒ y = 400
Putting y = 400 in (i), we get
6x + 2000 = 5600
⇒ 6x = 5600 − 2000 = 3600
⇒ x = 600
Hence, CP of saree = ₹600 and list price of sweater = ₹400.