A person marks his goods 35% above the cost price. He sells 40% of the goods…
2019
A person marks his goods 35% above the cost price. He sells 40% of the goods at the marked price, 25% at 8% discount and the remaining at x% discount. If his overall profit is 24.74%, what is the value of x?
- A.
16
- B.
15
- C.
18
- D.
20
Attempted by 52 students.
Show answer & explanation
Correct answer: A
When goods are sold in parts at different price points relative to a common Marked Price (MP), express each part's Selling Price as a fraction of MP, weight each fraction by the portion of goods sold, and equate the weighted sum to the revenue-to-MP ratio implied by the target overall profit — then solve for the unknown discount.
MP = 1.35 × CP (35% markup); target revenue = 1.2474 × CP (24.74% profit) ⇒ target ratio = revenue/MP = 1.2474/1.35 = 0.924.
Portions: 40% at full MP → ratio 1; 25% at 8% discount → ratio 0.92; remaining 35% at x% discount → ratio (1 − x/100).
Weighted-average equation: 0.40×1 + 0.25×0.92 + 0.35×(1 − x/100) = 0.924.
Simplify: 0.98 − 0.0035x = 0.924 ⇒ 0.0035x = 0.056 ⇒ x = 16.
Check: at x = 16, revenue/MP = 0.924, so revenue = 0.924 × 135 = 124.74 on a cost of 100 — a 24.74% profit, confirming x = 16.
A video solution is available for this question — log in and enroll to watch it.