A man marks his goods at 60% above cost price. He sells 40% of the goods at…
2019
A man marks his goods at 60% above cost price. He sells 40% of the goods at 10% discount, 35% at 20% discount and the remaining at x% discount. If his overall profit is 30.4%, find x.
- A.
35%
- B.
40%
- C.
30%
- D.
25%
Attempted by 24 students.
Show answer & explanation
Correct answer: C
Let CP = 100 → MP = 160. Profits per item: 40% at 10% discount: SP = 160×0.9 = 144 → profit = 44.
35% at 20% discount: SP = 160×0.8 = 128 → profit = 28.
25% at x% discount: SP = 160(1 − x/100) → profit = 160(1 − x/100) − 100 = 60 − 1.6x.
Overall profit% = 0.4×44 + 0.35×28 + 0.25×(60 − 1.6x) = 17.6 + 9.8 + 15 − 0.4x = 42.4 − 0.4x Set = 30.4 ⇒ 42.4 − 0.4x = 30.4 ⇒ 0.4x = 12 ⇒ x = 30.