A businessman sells 60% of his wares at a profit of 15%. The remainder is sold at a loss of 25%. What is the percentage profit or loss on the sale of the whole wares?

Here are the solutions to your questions. Question 1: A businessman sells 60% of his wares at a profit of 15%. The remainder is sold at a loss of 25%. What is the percentage profit or loss on the sale of the whole wares? Step 1: Calculate the selling price for the first 60% of wares. Let the total cost price of the wares be C. The cost price of 60% of the wares is 0.60C. The profit on this portion is 15%, so the selling price (SP_1) is: SP_1 = 0.60C × (1 + 0.15) = 0.60C × 1.15 = 0.69C Step 2: Calculate the selling price for the remaining 40% of wares. The remainder is 100\% - 60\% = 40\% of the wares. The cost price of this portion is 0.40C. The loss on this portion is 25%, so the selling price (SP_2) is: SP_2 = 0.40C × (1 - 0.25) = 0.40C × 0.75 = 0.30C Step 3: Calculate the total selling price and compare it to the total cost price. The total selling price (SP_total) is the sum of SP_1 and SP_2: SP_total = 0.69C + 0.30C = 0.99C The total cost price is C. Since SP_total = 0.99C is less than C, there is an overall loss. Step 4: Calculate the percentage loss. The total loss is C - 0.99C = 0.01C. The percentage loss is: Percentage Loss = LossTotal Cost Price × 100\% Percentage Loss = (0.01C)/(C) × 100\% = 0.01 × 100\% = 1\% The percentage profit or loss on the sale of the whole wares is a 1% loss. Question 2: The coordinates of the vertices of a parallelogram are A(-2, 3), B(2, -1), C(5, 0) and D(m, n). a) Find AB and DC. Step 1: Find vector AB. To find AB, subtract the coordinates of A from B: AB = B - A = (2 - (-2), -1 - 3) = (2 + 2, -1 - 3) = (4, -4) Step 2: Find vector DC. To find DC, subtract the coordinates of D from C: DC = C - D = (5 - m, 0 - n) = (5 - m, -n) So, AB = (4, -4) and DC = (5 - m, -n). b) Find the coordinates of D. Step 3: Use the property of a parallelogram that opposite sides are equal and parallel. For a parallelogram ABCD, AB = DC. Equating the components of the vectors from Step 1 and Step 2: (4, -4) = (5 - m, -n) Equating the x-components: 4 = 5 - m m = 5 - 4 m = 1 Equating the y-components: -4 = -n n = 4 The coordinates of D are (1, 4). c) Calculate |DB| correct to one decimal place. Step 4: Calculate the distance between points D and B. The coordinates are D(1, 4) and B(2, -1). The distance formula is sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). |DB| = sqrt((2 - 1)^2 + (-1 - 4)^2) |DB| = sqrt((1)^2 + (-5)^2) |DB| = sqrt(1 + 25) |DB| = sqrt(26) Calculating the numerical value and rounding to one decimal place: |DB| ≈ 5.0990195... |DB| ≈ 5.1 Drop the next question! 📸