A person marks his goods, 60% above cost price. He sells 40% goods at 10%…
2019
A person marks his goods, 60% above cost price. He sells 40% goods at 10% discount, 35% goods at 20% discount and remaining at x% discount. If his overall profit percent is 30.4%, who is the value of x?
- A.
30%
- B.
25%
- C.
40%
- D.
35%
Attempted by 48 students.
Show answer & explanation
Correct answer: A
Solution
Assume total cost price = ₹100 (so cost per unit = ₹1 if we take 100 units). Marked price is 60% above cost, so marked price per unit = ₹1.60.
Sales breakdown and revenues:
40% of goods → 40 units at 10% discount: SP per unit = 1.60 × 0.90 = ₹1.44. Revenue = 40 × 1.44 = ₹57.60.
35% of goods → 35 units at 20% discount: SP per unit = 1.60 × 0.80 = ₹1.28. Revenue = 35 × 1.28 = ₹44.80.
Remaining 25% → 25 units at x% discount: SP per unit = 1.60 × (1 − x/100). Revenue = 25 × 1.60 × (1 − x/100) = 40 × (1 − x/100).
Total revenue = 57.60 + 44.80 + 40 × (1 − x/100) = 102.40 + 40 − 0.4x = 142.40 − 0.4x.
Given overall profit is 30.4% on cost ₹100, so total revenue must be ₹130.40.
Set up the equation: 142.40 − 0.4x = 130.40.
Solve: 0.4x = 142.40 − 130.40 = 12 ⇒ x = 12 / 0.4 = 30.
Answer: x = 30% discount.