A bag is sold at a certain price. If it is sold at 23 1/3% of this price,…
2020
A bag is sold at a certain price. If it is sold at 23 1/3% of this price, there is a loss of 33 1/3%. What is the percentage profit when it is sold at 56% of the original selling price?
- A.
40
- B.
60
- C.
75
- D.
50
Attempted by 2 students.
Show answer & explanation
Correct answer: B
CONCEPT: In profit-and-loss problems, every selling price must be compared on the cost-price base. If the loss is L%, then selling price = (100 - L)% of cost price; profit percent = (selling price - cost price) / cost price × 100.
APPLICATION:
Let the original selling price be S.
23 1/3% = 7/30, so the reduced selling price is 7S/30.
A loss of 33 1/3% leaves 66 2/3% = 2/3 of the cost price, so 7S/30 = 2CP/3.
Therefore CP = (7S/30) × (3/2) = 7S/20.
The later selling price is 56% of S = 14S/25.
Profit = 14S/25 - 7S/20 = 56S/100 - 35S/100 = 21S/100.
Profit percent = (21S/100) / (7S/20) × 100 = 60%.
CROSS-CHECK: CP is 35% of S and the later selling price is 56% of S; the gain over the cost base is (56 - 35) / 35 × 100 = 60%.
Result: The profit percentage is 60%.