A shopkeeper sells a saree at 8% profit and a sweater at 10% discount to get Rs 1008 in total. If instead she sells the saree at 10% profit and the sweater at 8% discount, she gets Rs 1028. Find the cost price of the saree and the list price of the sweater.
Saree (cost price) = Rs 600; Sweater (list price) = Rs 400.
Step 1: Assume variables
Let the cost price of the saree = \(S\).
Let the list price of the sweater = \(L\).
Step 2: Write equation for first case
The saree is sold at 8% profit. So selling price of saree = \(S + 8\%\text{ of }S = 1.08S\).
The sweater is sold at 10% discount. So selling price of sweater = \(L - 10\%\text{ of }L = 0.90L\).
Total money = Rs 1008.
Equation (1): \(1.08S + 0.90L = 1008\).
Step 3: Write equation for second case
Saree is sold at 10% profit. So selling price of saree = \(1.10S\).
Sweater is sold at 8% discount. So selling price of sweater = \(0.92L\).
Total money = Rs 1028.
Equation (2): \(1.10S + 0.92L = 1028\).
Step 4: Subtract the two equations
Equation (2) − Equation (1):
\((1.10S - 1.08S) + (0.92L - 0.90L) = 1028 - 1008\)
\(0.02S + 0.02L = 20\).
Divide both sides by 0.02: \(S + L = 1000\).
Step 5: Put this value in Equation (1)
From step 4, \(L = 1000 - S\).
Substitute into Equation (1):
\(1.08S + 0.90(1000 - S) = 1008\).
Simplify: \(1.08S + 900 - 0.90S = 1008\).
\(0.18S + 900 = 1008\).
\(0.18S = 108\).
\(S = 600\).
Step 6: Find \(L\)
\(L = 1000 - S = 1000 - 600 = 400\).
Final Answer: Saree cost price = Rs 600, Sweater list price = Rs 400.