A trader wants 10% profit on the selling price of a product whereas his…
2023
A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should be his rate of mark up on an article costing Rs. 12?
- A.
20 %
- B.
30 %
- C.
100 / 3 %
- D.
68 / 7 %
Show answer & explanation
Correct answer: C
When profit and expenses are both stated as percentages of the SELLING PRICE (not the cost price), you cannot add the percentages directly to the cost. Instead, treat the selling price (SP) as the unknown: SP = Cost Price + (profit % of SP) + (expenses % of SP). Solve this equation for SP; the rate of mark up is then always found on the COST PRICE: Markup % = [(SP − CP)/CP] × 100.
Let the selling price be SP (unknown) and the cost price CP = Rs. 12.
Profit = 10% of SP = 0.10·SP (profit is on the selling price, not the cost price).
Expenses = 15% of SP = 0.15·SP (expenses are on sales, i.e. on the selling price).
Selling price equation: SP = CP + profit + expenses ⇒ SP = 12 + 0.10·SP + 0.15·SP.
Collect the SP terms: SP − 0.25·SP = 12 ⇒ 0.75·SP = 12.
Solve: SP = 12 / 0.75 = Rs. 16.
Rate of markup (always on cost price) = [(SP − CP)/CP] × 100 = [(16 − 12)/12] × 100 = (4/12) × 100 = 100/3 %.
Cross-check: at SP = 16, profit = 10% of 16 = 1.6 and expenses = 15% of 16 = 2.4; CP + profit + expenses = 12 + 1.6 + 2.4 = 16 = SP, confirming SP = 16 and the markup of 100/3 % (≈ 33.33%).