A shopkeeper sells a saree at 8% profit and a sweater at 10% discount,

1.	A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting asum Rs.1008. If she had sold the saree at 10% profit and the sweater at 8% discount, shewould have got Rs1028. Find the cost price of the saree and the list price (price beforediscount) of the sweater.12,
Answer» Let the CP of saree and that of sweater be x and y respectively. Case 1. Given that saree is sold at 8% profit => SP of saree = x + 8x/100 = 108x/100 Also, sweater is sold at 10% discount => SP of sweater = y - 10y/100 = 9y/10 Given that saree and sweater fetch Rs 1008, 108x/100 + 9y/10 = 1008 => 108x+90y/100 = 1008 => 108x + 90y = 100800 => 6x + 5y = 5600 => x = 5600-5y/6 (i) Case 2. Given that saree is sold at 10% profit SP of saree = x + 10x/00 = 11x/10 Also, sweater is sold at 8% discount => SP of sweater = y - 8y/100 = 92y/100 = Given that saree and sweater fetch Rs 1028, 11x/10 + 92y/100 = 1028 => 110x+92y/100 = 1028 => 110x+92y = 102800 Putting value of (i) 110 (5600-5y/6) + 92y = 102800 => 616000-550y/6 + 92y = 102800 => 616000-550y-552y/6 = 102800 => 616000+2y/6 = 102800 => 616000+2y = 616800 => 2y = 800 =>y = Rs400 From (i), x = 5600 - 5*400/6 x = 5600-1200/6 x = 4200/6 => x = Rs700 Therefore, SP of saree = Rs700 List price of sweater = Rs 400

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting asum Rs.1008. If she had sold the saree at 10% profit and the sweater at 8% discount, shewould have got Rs1028. Find the cost price of the saree and the list price (price beforediscount) of the sweater.12,

Answer»

Let the CP of saree and that of sweater be x and y respectively.

Case 1.

Given that saree is sold at 8% profit

=> SP of saree = x + 8x/100 = 108x/100

Also, sweater is sold at 10% discount

=> SP of sweater = y - 10y/100 = 9y/10

Given that saree and sweater fetch Rs 1008,

108x/100 + 9y/10 = 1008

=> 108x+90y/100 = 1008

=> 108x + 90y = 100800 => 6x + 5y = 5600 => x = 5600-5y/6 (i)

Case 2.

Given that saree is sold at 10% profit

SP of saree = x + 10x/00 = 11x/10

Also, sweater is sold at 8% discount

=> SP of sweater = y - 8y/100 = 92y/100 =

Given that saree and sweater fetch Rs 1028,

11x/10 + 92y/100 = 1028

=> 110x+92y/100 = 1028

=> 110x+92y = 102800

Putting value of (i)

110 (5600-5y/6) + 92y = 102800

=> 616000-550y/6 + 92y = 102800

=> 616000-550y-552y/6 = 102800

=> 616000+2y/6 = 102800

=> 616000+2y = 616800

=> 2y = 800

=>y = Rs400

From (i),

x = 5600 - 5*400/6

x = 5600-1200/6

x = 4200/6

=> x = Rs700

Therefore, SP of saree = Rs700

List price of sweater = Rs 400